1) A population is a set that includes all elements about which we wish to draw a conclusion.
Answer: TRUE
Difficulty: 1 Easy
Topic: Populations, Samples, and Traditional Statistics
Learning Objective: 01-07 Describe the difference between a population and a sample.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
2) If we examine some of the population measurements, we are conducting a census of the
population.
Answer: FALSE
Explanation: A census is defined as examining all of the population measurements.
Difficulty: 2 Medium
Topic: Populations, Samples, and Traditional Statistics
Learning Objective: 01-07 Describe the difference between a population and a sample.
Bloom's: Understand
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
3) A random sample is selected so that every element in the population has the same chance of
being included in the sample.
Answer: TRUE
Difficulty: 1 Easy
Topic: Random Sampling and Three Case Studies That Illustrate Statistical Inference
Learning Objective: 01-09 Explain the concept of random sampling and select a random sample.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
1
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written consent of McGraw-Hill Education.
4) An example of a quantitative variable is the manufacturer of a car.
Answer: FALSE
Explanation: This is an example of a qualitative or categorical variable.
Difficulty: 1 Easy
Topic: Data
Learning Objective: 01-02 Describe the difference between a quantitative variable and a
qualitative variable.
Bloom's: Understand
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
5) An example of a qualitative variable is the mileage of a car.
Answer: FALSE
Explanation: This is an example of a quantitative variable.
Difficulty: 1 Easy
Topic: Data
Learning Objective: 01-02 Describe the difference between a quantitative variable and a
qualitative variable.
Bloom's: Understand
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
6) Statistical inference is the science of using a sample of measurements to make generalizations
about the important aspects of a population of measurements.
Answer: TRUE
Difficulty: 2 Medium
Topic: Populations, Samples, and Traditional Statistics
Learning Objective: 01-08 Distinguish between descriptive statistics and statistical inference.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
7) Time series data are data collected at the same time period.
Answer: FALSE
Explanation: Time series data are collected over different time periods.
Difficulty: 1 Easy
Topic: Data
Learning Objective: 01-03 Describe the difference between cross-sectional data and time series
data.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
2
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written consent of McGraw-Hill Education.
8) Cross-sectional data are data collected at the same or approximately the same point in time.
Answer: TRUE
Difficulty: 1 Easy
Topic: Data
Learning Objective: 01-03 Describe the difference between cross-sectional data and time series
data.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
9) Daily high temperature in a local community collected over a 30-day time period is an
example of cross-sectional data.
Answer: FALSE
Explanation: Cross-sectional data are collected at the same point in time. This is an example of
time series data.
Difficulty: 1 Easy
Topic: Data
Learning Objective: 01-03 Describe the difference between cross-sectional data and time series
data.
Bloom's: Understand
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
10) The number of sick days taken by employees in 2008 for the top 10 technology companies is
an example of time series data.
Answer: FALSE
Explanation: This is an example of cross-sectional data. Time series data are collected at
different time periods.
Difficulty: 1 Easy
Topic: Data
Learning Objective: 01-03 Describe the difference between cross-sectional data and time series
data.
Bloom's: Understand
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
3
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written consent of McGraw-Hill Education.
11) The number of sick days per month taken by employees for the last 10 years at Apex Co. is
an example of time series data.
Answer: TRUE
Difficulty: 2 Medium
Topic: Data
Learning Objective: 01-03 Describe the difference between cross-sectional data and time series
data.
Bloom's: Understand
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
12) A quantitative variable can also be referred to as a categorical variable.
Answer: FALSE
Explanation: Qualitative variables are also known as categorical variables.
Difficulty: 1 Easy
Topic: Data
Learning Objective: 01-02 Describe the difference between a quantitative variable and a
qualitative variable.
Bloom's: Understand
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
13) In a data set of information on college business students, an example of an element is their
cumulative GPA.
Answer: FALSE
Explanation: The college business students are the elements of the data set. The cumulative
GPA is an example of a variable, which is a characteristic of an element (i.e., a college business
student) in the data set.
Difficulty: 2 Medium
Topic: Data
Learning Objective: 01-01 Define a variable.
Bloom's: Understand
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
4
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written consent of McGraw-Hill Education.
14) In an observational study, the variable of interest is called a response variable.
Answer: TRUE
Difficulty: 1 Easy
Topic: Data Sources, Data Warehousing, and Big Data
Learning Objective: 01-05 Identify the different types of data sources: existing data sources,
experimental studies, and observational studies.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
15) In an experimental study, the aim is to manipulate or set the value of the response variable.
Answer: FALSE
Explanation: In experimental studies, the aim is to manipulate the factor(s), which may be
related to the response variable.
Difficulty: 2 Medium
Topic: Data Sources, Data Warehousing, and Big Data
Learning Objective: 01-05 Identify the different types of data sources: existing data sources,
experimental studies, and observational studies.
Bloom's: Understand
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
16) The science of describing the important aspects of a set of measures is called statistical
inference.
Answer: FALSE
Explanation: This is the definition of descriptive statistics. Statistical inference is the science of
using a sample of measurements to make generalizations about the population of measurements.
Difficulty: 2 Medium
Topic: Populations, Samples, and Traditional Statistics
Learning Objective: 01-08 Distinguish between descriptive statistics and statistical inference.
Bloom's: Understand
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
5
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written consent of McGraw-Hill Education.
17) It is possible to use a random sample from a population to make statistical inferences about
the entire population.
Answer: TRUE
Difficulty: 1 Easy
Topic: Populations, Samples, and Traditional Statistics
Learning Objective: 01-08 Distinguish between descriptive statistics and statistical inference.
Bloom's: Understand
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
18) Processes produce outputs over time.
Answer: TRUE
Difficulty: 1 Easy
Topic: Random Sampling and Three Case Studies That Illustrate Statistical Inference
Learning Objective: 01-09 Explain the concept of random sampling and select a random sample.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
19) Selecting many different samples and running many different tests can eventually produce a
result that makes a desired conclusion be true.
Answer: FALSE
Explanation: Using different samples and tests to produce a desired conclusion does not make
the conclusion true.
Difficulty: 2 Medium
Topic: Random Sampling and Three Case Studies That Illustrate Statistical Inference
Learning Objective: 01-09 Explain the concept of random sampling and select a random sample.
Bloom's: Understand
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
20) Using a nonrandom sample procedure in order to support a desired conclusion is an example
of an unethical statistical procedure.
Answer: TRUE
Difficulty: 2 Medium
Topic: Random Sampling and Three Case Studies That Illustrate Statistical Inference
Learning Objective: 01-09 Explain the concept of random sampling and select a random sample.
Bloom's: Understand
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
6
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written consent of McGraw-Hill Education.
21) An individual collecting data directly through planned experimentation is obtaining primary
data.
Answer: TRUE
Difficulty: 1 Easy
Topic: Data Sources, Data Warehousing, and Big Data
Learning Objective: 01-05 Identify the different types of data sources: existing data sources,
experimental studies, and observational studies.
Bloom's: Understand
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
22) Secondary data are data taken from an existing source.
Answer: TRUE
Difficulty: 1 Easy
Topic: Data Sources, Data Warehousing, and Big Data
Learning Objective: 01-05 Identify the different types of data sources: existing data sources,
experimental studies, and observational studies.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
23) Data warehousing is defined as a process of centralized data management and retrieval.
Answer: TRUE
Difficulty: 1 Easy
Topic: Data Sources, Data Warehousing, and Big Data
Learning Objective: 01-06 Explain the basic ideas of data warehousing and big data.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
24) The term big data refers to the use of survey data by big business.
Answer: FALSE
Explanation: Big data is a term that arose from the huge capacity of data warehouses that
contain massive amounts of data.
Difficulty: 1 Easy
Topic: Data Sources, Data Warehousing, and Big Data
Learning Objective: 01-06 Explain the basic ideas of data warehousing and big data.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
7
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written consent of McGraw-Hill Education.
25) In order to select a stratified random sample, we divide the population into overlapping
groups of similar elements.
Answer: FALSE
Explanation: A stratified random sample is created by dividing the population into nonoverlapping groups.
Difficulty: 2 Medium
Topic: Stratified Random, Cluster, and Systematic Sampling
Learning Objective: 01-12 Describe the basic ideas of stratified random, cluster, and systematic
sampling.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
26) If we sample without replacement, we do not place the unit chosen on a particular selection
back into the population.
Answer: TRUE
Difficulty: 2 Medium
Topic: Random Sampling and Three Case Studies That Illustrate Statistical Inference
Learning Objective: 01-09 Explain the concept of random sampling and select a random sample.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
27) By taking a systematic sample in which we select every 100th shopper arriving at a specific
store, we are approximating a random sample of shoppers.
Answer: TRUE
Difficulty: 2 Medium
Topic: Stratified Random, Cluster, and Systematic Sampling
Learning Objective: 01-12 Describe the basic ideas of stratified random, cluster, and systematic
sampling.
Bloom's: Understand
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
8
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written consent of McGraw-Hill Education.
28) A common practice in selecting a sample from a large geographic area is multistage cluster
sampling.
Answer: TRUE
Difficulty: 2 Medium
Topic: Stratified Random, Cluster, and Systematic Sampling
Learning Objective: 01-12 Describe the basic ideas of stratified random, cluster, and systematic
sampling.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
29) Stratification can at times be combined with multistage cluster sampling to develop an
appropriate sample.
Answer: TRUE
Difficulty: 2 Medium
Topic: Stratified Random, Cluster, and Systematic Sampling
Learning Objective: 01-12 Describe the basic ideas of stratified random, cluster, and systematic
sampling.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
30) In systematic sampling, the first element is randomly selected from the first (N/n) elements.
Answer: TRUE
Difficulty: 3 Hard
Topic: Stratified Random, Cluster, and Systematic Sampling
Learning Objective: 01-12 Describe the basic ideas of stratified random, cluster, and systematic
sampling.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
31) A sampling error can occur because of incomplete information.
Answer: TRUE
Difficulty: 2 Medium
Topic: More about Surveys and Errors in Survey Sampling
Learning Objective: 01-13 Describe basic types of survey questions, survey procedures, and
sources of error.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
32) The target population is the result of sampling from the original population that is of interest
9
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written consent of McGraw-Hill Education.
to the researcher.
Answer: FALSE
Explanation: Target population is the entire population of interest.
Difficulty: 2 Medium
Topic: More about Surveys and Errors in Survey Sampling
Learning Objective: 01-13 Describe basic types of survey questions, survey procedures, and
sources of error.
Bloom's: Understand
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
33) Errors of non-observation occur when data values are recorded incorrectly.
Answer: FALSE
Explanation: Errors of non-observation relate to population elements that are not observed.
Difficulty: 2 Medium
Topic: More about Surveys and Errors in Survey Sampling
Learning Objective: 01-13 Describe basic types of survey questions, survey procedures, and
sources of error.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
34) A recording error is an error of observation.
Answer: TRUE
Difficulty: 2 Medium
Topic: More about Surveys and Errors in Survey Sampling
Learning Objective: 01-13 Describe basic types of survey questions, survey procedures, and
sources of error.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
10
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written consent of McGraw-Hill Education.
35) A low response rate has no effect on the validity of a survey's findings.
Answer: FALSE
Explanation: Low response rates do affect the validity of a survey's results.
Difficulty: 2 Medium
Topic: More about Surveys and Errors in Survey Sampling
Learning Objective: 01-13 Describe basic types of survey questions, survey procedures, and
sources of error.
Bloom's: Understand
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
36) Sampling error occurs because a characteristic of a random sample may not exactly equal the
population characteristic that we are attempting to estimate.
Answer: TRUE
Difficulty: 2 Medium
Topic: More about Surveys and Errors in Survey Sampling
Learning Objective: 01-13 Describe basic types of survey questions, survey procedures, and
sources of error.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
37) Convenience sampling is a type of probability sampling in which we select elements to
sample because we believe they have the highest probability of responding.
Answer: FALSE
Explanation: Convenience sampling is not probability sampling. Convenience sampling is a type
of sampling in which we select elements because they are easy or convenient to sample.
Difficulty: 2 Medium
Topic: Random Sampling and Three Case Studies That Illustrate Statistical Inference
Learning Objective: 01-09 Explain the concept of random sampling and select a random sample.
Bloom's: Understand
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
11
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written consent of McGraw-Hill Education.
38) Judgment sampling is an example of convenience sampling.
Answer: FALSE
Explanation: Judgment sampling has an extremely knowledgeable individual select the sample.
Voluntary sampling occurs when participants self-select, which is a form of convenience
sampling, where elements are selected because they are easy or convenient to sample.
Difficulty: 2 Medium
Topic: Random Sampling and Three Case Studies That Illustrate Statistical Inference
Learning Objective: 01-09 Explain the concept of random sampling and select a random sample.
Bloom's: Understand
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
39) Judgment sampling occurs when a person who is extremely knowledgeable about the
population under consideration selects the population elements that they feel are most
representative of the population.
Answer: TRUE
Difficulty: 1 Easy
Topic: Random Sampling and Three Case Studies That Illustrate Statistical Inference
Learning Objective: 01-09 Explain the concept of random sampling and select a random sample.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
40) Business analytics is a new field that does not use traditional statistics to analyze big data.
Answer: FALSE
Explanation: Business analytics is an extension of traditional statistics.
Difficulty: 2 Medium
Topic: Business Analytics and Data Mining
Learning Objective: 01-10 Explain some of the uses of business analytics and data mining.
Bloom's: Understand
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
12
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written consent of McGraw-Hill Education.
41) Prescriptive analytics involve methods used to find anomalies, patterns, and associations in
data sets with the purpose of predicting future outcomes.
Answer: FALSE
Explanation: This is the definition of predictive analytics. Prescriptive analytics uses results
from predictive analytics to recommend courses of action within the business.
Difficulty: 2 Medium
Topic: Business Analytics and Data Mining
Learning Objective: 01-10 Explain some of the uses of business analytics and data mining.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
42) A population that consists of all the customers who will use the drive-thru of the local fast
food restaurant is called a(n) ________.
A) infinite population
B) random sample population
C) statistical population
D) finite population
Answer: D
Explanation: It is a finite population because only a finite number of customers will use the
drive-thru. An infinite population would be defined as the theoretical potential number of
customers.
Difficulty: 2 Medium
Topic: Random Sampling and Three Case Studies That Illustrate Statistical Inference
Learning Objective: 01-09 Explain the concept of random sampling and select a random sample.
Bloom's: Understand
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
43) In ________ we select elements because they are easy to sample.
A) random sampling
B) convenience sampling
C) judgment sampling
D) probability sampling
Answer: B
Explanation: Random sampling, judgment sampling, and probability sampling are methods of
sampling in which the selected elements may not be convenient to sample.
Difficulty: 1 Easy
Topic: Random Sampling and Three Case Studies That Illustrate Statistical Inference
Learning Objective: 01-09 Explain the concept of random sampling and select a random sample.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
13
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written consent of McGraw-Hill Education.
44) ________ sampling is where we know the chance that each element will be included in the
sample, which allows us to make statistical inferences about the sample population.
A) Convenience
B) Voluntary
C) Probability
D) Judgment
Answer: C
Explanation: Convenience, voluntary, and judgment sampling should not be used to make valid
statistical inferences about a population.
Difficulty: 2 Medium
Topic: Random Sampling and Three Case Studies That Illustrate Statistical Inference
Learning Objective: 01-09 Explain the concept of random sampling and select a random sample.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
45) Which of the following is not a method of numerical descriptive analytics?
A) factor analysis
B) cluster analysis
C) bullet graphs
D) association learning
Answer: C
Explanation: Bullet graphs are a method of graphical descriptive analytics.
Difficulty: 2 Medium
Topic: Business Analytics and Data Mining
Learning Objective: 01-10 Explain some of the uses of business analytics and data mining.
Bloom's: Understand
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
14
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written consent of McGraw-Hill Education.
46) ________ uses traditional or newer graphics to present visual summaries of business
information.
A) Nonparametric predictive analytics
B) Parametric predictive analytics
C) Prescriptive analytics
D) Graphical descriptive analytics
Answer: D
Explanation: Predictive analytics (whether parametric or nonparametric) are methods used to
predict values of a response variable on the basis of one or more predictor variables. Prescriptive
analytics are techniques that combine external and internal constraints with results from
descriptive or predictive analytics to recommend an optimal course of action.
Difficulty: 1 Easy
Topic: Business Analytics and Data Mining
Learning Objective: 01-10 Explain some of the uses of business analytics and data mining.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
47) Which of the following is not a supervised learning technique in predictive analytics?
A) linear regression
B) factor analysis
C) decision trees
D) neural networks
Answer: B
Explanation: Factor analysis is an unsupervised learning technique because there is no specific
response variable involved, which is a requirement for a supervised learning technique.
Difficulty: 2 Medium
Topic: Business Analytics and Data Mining
Learning Objective: 01-10 Explain some of the uses of business analytics and data mining.
Bloom's: Understand
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
15
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written consent of McGraw-Hill Education.
48) Transactional data are now used by businesses as part of
A) survey analysis.
B) big data.
C) descriptive statistics.
D) experimental studies.
Answer: B
Explanation: By definition, big data are collected by business for effective decision making.
Difficulty: 2 Medium
Topic: Data Sources, Data Warehousing, and Big Data
Learning Objective: 01-06 Explain the basic ideas of data warehousing and big data.
Bloom's: Understand
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
49) ________ consists of a set of concepts and techniques that are used to describe populations
and samples and to make statistical inferences about populations by using samples.
A) Traditional statistics
B) Random sampling
C) Data mining
D) Time series analysis
Answer: A
Explanation: Definition of traditional statistics.
Difficulty: 1 Easy
Topic: Populations, Samples, and Traditional Statistics
Learning Objective: 01-08 Distinguish between descriptive statistics and statistical inference.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
16
Copyright 2019 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior
written consent of McGraw-Hill Education.
50) When we are choosing a random sample and we do not place chosen units back into the
population, we are
A) sampling with replacement.
B) sampling without replacement.
C) using a systematic sample.
D) using a voluntary response sample.
Answer: B
Explanation: Sampling with replacement occurs when a selected element is replaced before
another sample is taken; systematic and voluntary response samples are not random.
Difficulty: 2 Medium
Topic: Random Sampling and Three Case Studies That Illustrate Statistical Inference
Learning Objective: 01-09 Explain the concept of random sampling and select a random sample.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
51) Which of the following is a type of question used in survey research?
A) dichotomous
B) open-ended
C) multiple-choice
D) All of the other answers are correct.
Answer: D
Explanation: All three of the listed question types can be used in survey design.
Difficulty: 2 Medium
Topic: More about Surveys and Errors in Survey Sampling
Learning Objective: 01-13 Describe basic types of survey questions, survey procedures, and
sources of error.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
17
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written consent of McGraw-Hill Education.
52) Methods for obtaining a sample are called
A) sample surveys.
B) probability sampling.
C) random sampling.
D) sampling designs.
Answer: D
Explanation: Sample surveys are the result of sampling designs. Random sampling, stratified
random sampling, cluster sampling, and systematic sampling are sampling designs which are
types of probability sampling.
Difficulty: 2 Medium
Topic: Stratified Random, Cluster, and Systematic Sampling
Learning Objective: 01-12 Describe the basic ideas of stratified random, cluster, and systematic
sampling.
Bloom's: Understand
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
53) A ________ is a list of all the units in a population.
A) sample
B) frame
C) census
D) variable
Answer: B
Explanation: A sample can be only a part of a population; a census is the examination of the
population and variable is a characteristic of an element of the population.
Difficulty: 2 Medium
Topic: Random Sampling and Three Case Studies That Illustrate Statistical Inference
Learning Objective: 01-09 Explain the concept of random sampling and select a random sample.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
18
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written consent of McGraw-Hill Education.
54) Nonoverlapping groups of similar elements in a population are called
A) clusters.
B) frames.
C) strata.
D) stages.
Answer: C
Explanation: Strata are groups within a population sample which do not overlap.
Difficulty: 3 Hard
Topic: Stratified Random, Cluster, and Systematic Sampling
Learning Objective: 01-12 Describe the basic ideas of stratified random, cluster, and systematic
sampling.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
55) A Yes or No question is ________.
A) dichotomous
B) evaluative
C) open-ended
D) systematic
Answer: A
Explanation: Dichotomous questions consist of only two possible responses.
Difficulty: 2 Medium
Topic: More about Surveys and Errors in Survey Sampling
Learning Objective: 01-13 Describe basic types of survey questions, survey procedures, and
sources of error.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
19
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written consent of McGraw-Hill Education.
56) ________ occurs when some population elements are excluded from the process of selecting
the sample.
A) Nonresponse
B) Error of observation
C) Undercoverage
D) Sample frame
Answer: C
Explanation: Exclusion of population elements in selection is not a result of nonresponse or
error of observation because this occurs during the survey itself. Sampling error is a result of the
survey process.
Difficulty: 2 Medium
Topic: More about Surveys and Errors in Survey Sampling
Learning Objective: 01-13 Describe basic types of survey questions, survey procedures, and
sources of error.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
57) ________ is the difference between a numerical descriptor of the population and the
corresponding descriptor of the sample.
A) Sampling error
B) Nonobservation error
C) Observation error
D) Nonresponse
Answer: A
Explanation: Nonresponse, nonobservation and observation error occur during the survey
process. Sampling error is a result of the survey process.
Difficulty: 2 Medium
Topic: More about Surveys and Errors in Survey Sampling
Learning Objective: 01-13 Describe basic types of survey questions, survey procedures, and
sources of error.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
20
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written consent of McGraw-Hill Education.
58) Data that are collected by an individual through personally planned experimentation or
observation are ________.
A) secondary data
B) quantitative data
C) primary data
D) variables
Answer: C
Explanation: By definition, primary data are collected while secondary data are from an existing
source.
Difficulty: 1 Easy
Topic: Data Sources, Data Warehousing, and Big Data
Learning Objective: 01-05 Identify the different types of data sources: existing data sources,
experimental studies, and observational studies.
Bloom's: Understand
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
59) A ratio variable has the following characteristic.
A) qualitative
B) inherently defined zero value
C) categorical in nature
D) predictable
Answer: B
Explanation: By definition, ratio variables are quantitative and have an absolute zero value.
Difficulty: 1 Easy
Topic: Ratio, Interval, Ordinal, and Nominative Scales of Measurement
Learning Objective: 01-11 Identify the ratio, interval, ordinal, and nominative scales of
measurement.
Bloom's: Understand
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
21
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written consent of McGraw-Hill Education.
60) Which of the following is a quantitative variable?
A) the manufacturer of a cell phone
B) a person's gender
C) mileage of a car
D) whether a person is a college graduate
E) whether a person has a charge account
Answer: C
Explanation: A quantitative variable is measurable and noncategorical.
Difficulty: 1 Easy
Topic: Data
Learning Objective: 01-02 Describe the difference between a quantitative variable and a
qualitative variable.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
61) Which of the following is a categorical variable?
A) air temperature
B) bank account balance
C) daily sales in a store
D) whether a person has a traffic violation
E) value of company stock
Answer: D
Explanation: A categorical variable is qualitative, not measured.
Difficulty: 2 Medium
Topic: Data
Learning Objective: 01-02 Describe the difference between a quantitative variable and a
qualitative variable.
Bloom's: Understand
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
22
Copyright 2019 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior
written consent of McGraw-Hill Education.
62) Measurements from a population are called
A) elements.
B) observations.
C) variables.
D) processes.
Answer: B
Explanation: By definition, elements are the members of the population and variables are
characteristics of elements; a measurement (or observation) assigns a value to a variable for an
element of the population. A process is a sequence of operations that takes inputs and turns them
into outputs.
Difficulty: 2 Medium
Topic: Populations, Samples, and Traditional Statistics
Learning Objective: 01-07 Describe the difference between a population and a sample.
Bloom's: Understand
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
63) The two types of quantitative variables are
A) ordinal and ratio.
B) interval and ordinal.
C) nominative and ordinal.
D) interval and ratio.
E) nominative and interval.
Answer: D
Explanation: Nominative and ordinal are types of qualitative variables.
Difficulty: 2 Medium
Topic: Ratio, Interval, Ordinal, and Nominative Scales of Measurement
Learning Objective: 01-11 Identify the ratio, interval, ordinal, and nominative scales of
measurement.
Bloom's: Understand
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
23
Copyright 2019 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior
written consent of McGraw-Hill Education.
64) Temperature (in degrees Fahrenheit) is an example of a(n) ________ variable.
A) nominative
B) ordinal
C) interval
D) ratio
Answer: C
Explanation: Temperature is quantitative (excludes nominative and ordinal), and the ratio of two
temperatures is not meaningful.
Difficulty: 2 Medium
Topic: Ratio, Interval, Ordinal, and Nominative Scales of Measurement
Learning Objective: 01-11 Identify the ratio, interval, ordinal, and nominative scales of
measurement.
Bloom's: Understand
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
65) Jersey numbers of soccer players is an example of a(n) ________ variable.
A) nominative
B) ordinal
C) interval
D) ratio
Answer: A
Explanation: Interval and ratio are quantitative variables; jersey numbers have no logical order.
Difficulty: 2 Medium
Topic: Ratio, Interval, Ordinal, and Nominative Scales of Measurement
Learning Objective: 01-11 Identify the ratio, interval, ordinal, and nominative scales of
measurement.
Bloom's: Understand
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
24
Copyright 2019 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior
written consent of McGraw-Hill Education.
66) The weight of a chemical compound used in an experiment that is obtained using a welladjusted scale represents a(n) ________ level of measurement.
A) nominative
B) ordinal
C) interval
D) ratio
Answer: D
Explanation: Nominative and ordinal are qualitative variables; weight creates logical ratios: 60
lb is twice as heavy as 30 lb.
Difficulty: 2 Medium
Topic: Ratio, Interval, Ordinal, and Nominative Scales of Measurement
Learning Objective: 01-11 Identify the ratio, interval, ordinal, and nominative scales of
measurement.
Bloom's: Understand
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
67) An identification of police officers by rank would represent a(n) ________ level of
measurement.
A) nominative
B) ordinal
C) interval
D) ratio
Answer: B
Explanation: Interval and ratio are quantitative variables, nominative is only a naming category,
and police rank has order.
Difficulty: 2 Medium
Topic: Ratio, Interval, Ordinal, and Nominative Scales of Measurement
Learning Objective: 01-11 Identify the ratio, interval, ordinal, and nominative scales of
measurement.
Bloom's: Understand
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
25
Copyright 2019 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior
written consent of McGraw-Hill Education.
68) ________ is a necessary component of a runs plot.
A) Observation over time
B) Qualitative variable
C) Random sampling of the data
D) Cross-sectional data
Answer: A
Explanation: A runs plot is a graphical display of time series data.
Difficulty: 2 Medium
Topic: Data
Learning Objective: 01-04 Construct and interpret a time series (runs) plot.
Bloom's: Understand
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
69) ________ is the science of using a sample to make generalizations about the important
aspects of a population.
A) Time series analysis
B) Descriptive statistics
C) Random sample
D) Statistical inference
Answer: D
Explanation: By definition, a time series is a study of data over time; descriptive statistics is the
study of the measurements of population variables; a random sample is a data set.
Difficulty: 1 Easy
Topic: Populations, Samples, and Traditional Statistics
Learning Objective: 01-08 Distinguish between descriptive statistics and statistical inference.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
26
Copyright 2019 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior
written consent of McGraw-Hill Education.
70) College entrance exam scores, such as SAT scores, are an example of a(n) ________
variable.
A) ordinal
B) ratio
C) nominative
D) interval
Answer: D
Explanation: Nominative and ordinal are qualitative variables; college entrance exam scores
have no meaningful ratio and no inherently defined zero value.
Difficulty: 3 Hard
Topic: Ratio, Interval, Ordinal, and Nominative Scales of Measurement
Learning Objective: 01-11 Identify the ratio, interval, ordinal, and nominative scales of
measurement.
Bloom's: Understand
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
71) The number of miles a truck is driven before it is overhauled is an example of a(n) ________
variable.
A) nominative
B) ordinal
C) interval
D) ratio
Answer: D
Explanation: Nominative and ordinal are qualitative variables; miles driven can have a
meaningful ratio.
Difficulty: 2 Medium
Topic: Ratio, Interval, Ordinal, and Nominative Scales of Measurement
Learning Objective: 01-11 Identify the ratio, interval, ordinal, and nominative scales of
measurement.
Bloom's: Understand
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
27
Copyright 2019 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior
written consent of McGraw-Hill Education.
72) A(n) ________ variable is a qualitative variable such that there is no meaningful ordering or
ranking of the categories.
A) ratio
B) ordinal
C) nominative
D) interval
Answer: C
Explanation: Ratio and interval are quantitative variables; ordinal implies order or rank.
Difficulty: 1 Easy
Topic: Ratio, Interval, Ordinal, and Nominative Scales of Measurement
Learning Objective: 01-11 Identify the ratio, interval, ordinal, and nominative scales of
measurement.
Bloom's: Understand
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
73) A person's telephone area code is an example of a(n) ________ variable.
A) nominative
B) ordinal
C) interval
D) ratio
Answer: A
Explanation: This is a qualitative variable without order; therefore, a nominative variable.
Difficulty: 2 Medium
Topic: Ratio, Interval, Ordinal, and Nominative Scales of Measurement
Learning Objective: 01-11 Identify the ratio, interval, ordinal, and nominative scales of
measurement.
Bloom's: Understand
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
28
Copyright 2019 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior
written consent of McGraw-Hill Education.
74) Any characteristic of a population unit is a(n)
A) measurement.
B) sample.
C) observation.
D) variable.
Answer: D
Explanation: Measurement and observation are methods attached to a variable; a sample is a
subset of the units in a population.
Difficulty: 2 Medium
Topic: Data
Learning Objective: 01-01 Define a variable.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
75) Examining all population measurements is called a ________.
A) census
B) frame
C) sample
D) variable
Answer: A
Explanation: By definition, a census looks at the entire population.
Difficulty: 2 Medium
Topic: Populations, Samples, and Traditional Statistics
Learning Objective: 01-07 Describe the difference between a population and a sample.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
76) Any characteristic of an element is called a ________.
A) set
B) process
C) variable
D) census
Answer: C
Explanation: A process is a sequence of operations; a census looks at the entire population; set is
related to population.
Difficulty: 1 Easy
Topic: Data
Learning Objective: 01-01 Define a variable.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
29
Copyright 2019 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior
written consent of McGraw-Hill Education.
77) The process of assigning a value of a variable to each element in a data set is called
________.
A) sampling
B) measurement
C) experimental analysis
D) observational analysis
Answer: B
Explanation: By definition, sampling is taking a portion of the population to measure;
experimental and observational analysis are methods of obtaining data.
Difficulty: 2 Medium
Topic: Data
Learning Objective: 01-01 Define a variable.
Bloom's: Understand
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
78) A ________ is a display of individual measurements versus time.
A) runs plot
B) statistical analysis
C) random sample
D) measurement
Answer: A
Explanation: A runs plot is a graphical display of data over time.
Difficulty: 1 Easy
Topic: Data
Learning Objective: 01-04 Construct and interpret a time series (runs) plot.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
30
Copyright 2019 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior
written consent of McGraw-Hill Education.
79) Statistical ________ refers to using a sample of measurements and making generalizations
about the important aspects of a population.
A) sampling
B) process
C) analysis
D) inference
Answer: D
Explanation: By definition, inference is taking a sample of data and its measurements and
relating those measurements to the population as a whole.
Difficulty: 2 Medium
Topic: Populations, Samples, and Traditional Statistics
Learning Objective: 01-08 Distinguish between descriptive statistics and statistical inference.
Bloom's: Understand
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
80) A ________ is a subset of the units in a population.
A) census
B) process
C) sample
D) variable
Answer: C
Explanation: By definition, a census looks at an entire population; a variable is a characteristic
of an element within the population; a process is a sequence of operations that produces elements
of a population.
Difficulty: 1 Easy
Topic: Populations, Samples, and Traditional Statistics
Learning Objective: 01-07 Describe the difference between a population and a sample.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
31
Copyright 2019 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior
written consent of McGraw-Hill Education.
81) A ________ variable takes on values that are numbers on the real number line.
A) qualitative
B) quantitative
C) categorical
D) nominative
Answer: B
Explanation: Qualitative, categorical, and nominative variables are non-quantitative variables.
Difficulty: 2 Medium
Topic: Data
Learning Objective: 01-02 Describe the difference between a quantitative variable and a
qualitative variable.
Bloom's: Understand
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
82) A sequence of operations that takes inputs and turns them into outputs is a ________.
A) process
B) statistical inference
C) runs plot
D) random sampling
Answer: A
Explanation: By definition, a runs plot is a graphical display; random sampling is a method of
selecting a portion of a population; statistical inference is the science of using a sample of
measurements to infer about the entire population.
Difficulty: 1 Easy
Topic: Random Sampling and Three Case Studies That Illustrate Statistical Inference
Learning Objective: 01-09 Explain the concept of random sampling and select a random sample.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
32
Copyright 2019 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior
written consent of McGraw-Hill Education.
83) A(n) ________ variable can have values that indicate into which of several categories of a
population it belongs.
A) qualitative
B) quantitative
C) ratio
D) interval
Answer: A
Explanation: Quantitative, ratio, and interval all have similar definitions.
Difficulty: 2 Medium
Topic: Data
Learning Objective: 01-02 Describe the difference between a quantitative variable and a
qualitative variable.
Bloom's: Understand
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
84) A set of all elements we wish to study is called a ________.
A) sample
B) process
C) census
D) population
Answer: D
Explanation: By definition, a census is the examination of all population measurements; a
process is a sequence of operations; a sample is a subset of a population.
Difficulty: 2 Medium
Topic: Populations, Samples, and Traditional Statistics
Learning Objective: 01-07 Describe the difference between a population and a sample.
Bloom's: Understand
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
33
Copyright 2019 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior
written consent of McGraw-Hill Education.
85) ________ refers to describing the important aspects of a set of measurements.
A) Cross-sectional analysis
B) Runs plot
C) Descriptive statistics
D) Time series analysis
Answer: C
Explanation: A runs plot and time series analysis both look at data over time; cross-sectional
analysis looks at data collected at the same point in time.
Difficulty: 2 Medium
Topic: Populations, Samples, and Traditional Statistics
Learning Objective: 01-08 Distinguish between descriptive statistics and statistical inference.
Bloom's: Understand
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
86) The change in the daily price of a stock is what type of variable?
A) qualitative
B) ordinal
C) random
D) quantitative
Answer: D
Explanation: Qualitative and ordinal have similar definitions; random variables are all
characteristics of a population element.
Difficulty: 2 Medium
Topic: Data
Learning Objective: 01-02 Describe the difference between a quantitative variable and a
qualitative variable.
Bloom's: Understand
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
34
Copyright 2019 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior
written consent of McGraw-Hill Education.
87) Data collected for a particular study are referred to as a data ________.
A) variable
B) measurement
C) set
D) element
Answer: C
Explanation: By definition, a variable is a characteristic of an element; a measurement assigns a
value to a variable; an element is one unit of a population.
Difficulty: 2 Medium
Topic: Data
Learning Objective: 01-01 Define a variable.
Bloom's: Understand
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
88) A data set provides information about some group of individual ________.
A) variables
B) elements
C) statistics
D) measurements
Answer: B
Explanation: By definition, measurements assign values to a variable of an element; statistics is
the science of describing aspects of a set of measurements; variables are characteristics of
elements in a population.
Difficulty: 2 Medium
Topic: Data
Learning Objective: 01-01 Define a variable.
Bloom's: Understand
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
35
Copyright 2019 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior
written consent of McGraw-Hill Education.
89) When the data being studied are gathered from a published source, this is referred to as a(n)
________.
A) existing data source
B) observational data source
C) experimental data source
D) cross-sectional data source
Answer: A
Explanation: By definition, an experimental data source is a collection of data where one is able
to manipulate values; an observational data source is a collection of data where one is unable to
control factors. Cross-sectional is not a defined data source but rather a way of analyzing or
displaying the data that have been collected.
Difficulty: 2 Medium
Topic: Data Sources, Data Warehousing, and Big Data
Learning Objective: 01-05 Identify the different types of data sources: existing data sources,
experimental studies, and observational studies.
Bloom's: Understand
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
90) One method of being sure a sample being studied can be used to make statistical inferences
about the population is to select a
A) judgment sample.
B) voluntary response sample.
C) convenience sample.
D) probability sample.
Answer: D
Explanation: Runs plots are a way of looking at processes over time, which can then be used to
make inferences about a population. Simply looking at descriptive statistics (of which,
proportion and cross-sectional analysis are methods or procedures) is not sufficient to make
inferences.
Difficulty: 2 Medium
Topic: Random Sampling and Three Case Studies That Illustrate Statistical Inference
Learning Objective: 01-09 Explain the concept of random sampling and select a random sample.
Bloom's: Apply
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
36
Copyright 2019 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior
written consent of McGraw-Hill Education.
91) Which of the following is not an example of unethical statistical practices?
A) inappropriate interpretation of statistical results
B) using graphs to make statistical inferences
C) improper sampling
D) descriptive measures that mislead the user
E) None of the other answers is correct.
Answer: B
Explanation: It is unethical to use methods or procedures designed to mislead the audience that
is viewing the findings.
Difficulty: 2 Medium
Topic: Random Sampling and Three Case Studies That Illustrate Statistical Inference
Learning Objective: 01-09 Explain the concept of random sampling and select a random sample.
Bloom's: Understand
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
92) If we collect data on the number of wins each team in the NFL had during the 2011-12
season, we have ________ data.
A) cross-sectional
B) time series
C) non-historical
D) survey
Answer: A
Explanation: A time series is a collection of data taken over time, while a cross-section is a
collection of data taken at the same point in time.
Difficulty: 2 Medium
Topic: Data
Learning Objective: 01-03 Describe the difference between cross-sectional data and time series
data.
Bloom's: Understand
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
37
Copyright 2019 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior
written consent of McGraw-Hill Education.
93) If we collect data on the number of wins the Dallas Cowboys earned each of the past 10
years, we have ________ data.
A) cross-sectional
B) time series
C) non-historical
D) survey
Answer: B
Explanation: A time series is a collection of data taken over time, while a cross-section is a
collection of data taken at the same point in time.
Difficulty: 2 Medium
Topic: Data
Learning Objective: 01-03 Describe the difference between cross-sectional data and time series
data.
Bloom's: Understand
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
94) A study is being conducted on the effect of gas price on the number of miles driven in a
given month. Residents in two cities, one on the East Coast and one on the West Coast, are
randomly selected and asked to complete a questionnaire on the type of car they drive, the
number of miles they live from work, the number of children under 18 in their household, their
monthly income, and the number of miles they have driven over the past 30 days. List the
response variable(s).
Answer: The response variable in this study is the number of miles driven over the past 30 days.
Response variables are defined as the variable of interest in a study.
Difficulty: 2 Medium
Topic: Data Sources, Data Warehousing, and Big Data
Learning Objective: 01-05 Identify the different types of data sources: existing data sources,
experimental studies, and observational studies.
Bloom's: Understand; Apply
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
38
Copyright 2019 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior
written consent of McGraw-Hill Education.
95) A study is being conducted on the effect of gas price on the number of miles driven in a
given month. Residents in two cities, one on the East Coast and one on the West Coast, are
randomly selected and asked to complete a questionnaire on the type of car they drive, the
number of miles they live from work, the number of children under 18 in their household, their
monthly income, and the number of miles they have driven over the past 30 days. Is this an
experimental or observational study?
Answer: Observational study
An observational study occurs when analysts are unable to control the factors of interest. An
experimental study occurs when values of factors that are related to the variable of interest can
be set or manipulated.
Difficulty: 2 Medium
Topic: Data Sources, Data Warehousing, and Big Data
Learning Objective: 01-05 Identify the different types of data sources: existing data sources,
experimental studies, and observational studies.
Bloom's: Understand; Apply
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
96) A study is being conducted on the effect of gas price on the number of miles driven in a
given month. Residents in two cities, one on the East Coast and one on the West Coast, are
randomly selected and asked to complete a questionnaire on the type of car they drive, the
number of miles they live from work, the number of children under 18 in their household, their
monthly income, and the number of miles they have driven over the past 30 days. List the
factor(s).
Answer: Factors in this study are location of residence, type of car, number of miles from work,
number of children under 18, and monthly income.
Factors are related to the variable of interest.
Difficulty: 2 Medium
Topic: Data Sources, Data Warehousing, and Big Data
Learning Objective: 01-05 Identify the different types of data sources: existing data sources,
experimental studies, and observational studies.
Bloom's: Understand; Apply
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
39
Copyright 2019 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior
written consent of McGraw-Hill Education.
97) Looking at the runs plot of gasoline prices over the past 30 months, describe what it tells us
about the price of gas during these 30 months.
Answer:
The price of gas peaked in the seventh month. The lowest price is observed around 20 to 21
months from the start of the data collection. At the end of the 30 months, gas price is beginning
to show stability.
Observing the rise and fall of a time series or runs plot.
Difficulty: 2 Medium
Topic: Data
Learning Objective: 01-04 Construct and interpret a time series (runs) plot.
Bloom's: Understand; Apply
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
40
Copyright 2019 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior
written consent of McGraw-Hill Education.
98) Using the following data table of the average hours per week spent on Internet activities by
15- to 18-year-olds for the years 1999 to 2008, construct the runs plot and interpret.
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
13.5
15.0
16.5
17.7
18.2
19.3
19.5
19.9
20.1
20.4
Answer:
Displaying the average hours spent on Internet activities graphically results in a time series or
runs plot. An increase over time in the amount of time can be observed through either the graph
or data.
Difficulty: 2 Medium
Topic: Data
Learning Objective: 01-04 Construct and interpret a time series (runs) plot.
Bloom's: Understand; Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
41
Copyright 2019 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior
written consent of McGraw-Hill Education.
1) A stem-and-leaf display is a graphical portrayal of a data set that shows the data set's overall
pattern of variation.
Answer: TRUE
Explanation: This kind of graph places the measurements in order from smallest to largest.
Difficulty: 2 Medium
Topic: Stem-and-Leaf Displays
Learning Objective: 02-05 Construct and interpret stem-and-leaf displays.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
2) The relative frequency is the frequency of a class divided by the total number of
measurements.
Answer: TRUE
Explanation: This is used when we wish to summarize the proportion (or fraction) of items in
each class.
Difficulty: 2 Medium
Topic: Graphically Summarizing Qualitative Data; Graphically Summarizing Quantitative Data
Learning Objective: 02-03 Summarize quantitative data using frequency distributions,
histograms, frequency polygons, and ogives.; 02-01 Summarize qualitative data by using
frequency distributions, bar charts, and pie charts.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
3) A bar chart is a graphic that can be used to depict qualitative data.
Answer: TRUE
Explanation: A bar chart is a graphic that depicts a frequency, relative frequency, or percent
frequency distribution.
Difficulty: 1 Easy
Topic: Graphically Summarizing Qualitative Data
Learning Objective: 02-01 Summarize qualitative data by using frequency distributions, bar
charts, and pie charts.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
42
Copyright 2019 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior
written consent of McGraw-Hill Education.
4) Stem-and-leaf displays and dot plots are useful for detecting outliers.
Answer: TRUE
Explanation: Since this graph places the measurements in order from smallest to largest, it
allows the analyst to see all of the measurements in the data set.
Difficulty: 2 Medium
Topic: Stem-and-Leaf Displays; Dot Plots
Learning Objective: 02-05 Construct and interpret stem-and-leaf displays.; 02-04 Construct and
interpret dot plots.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
5) A scatter plot can be used to identify outliers.
Answer: FALSE
Explanation: A scatter plot is used to identify the relationship between two variables.
Difficulty: 2 Medium
Topic: Scatter Plots
Learning Objective: 02-07 Examine the relationships between variables by using scatter plots.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
6) When looking at the shape of the distribution using a histogram, a distribution is skewed to the
right when the left tail is shorter than the right tail.
Answer: TRUE
Explanation: This type of histogram has a high frequency number of data points on the right
compared to the left side of the histogram.
Difficulty: 2 Medium
Topic: Graphically Summarizing Quantitative Data
Learning Objective: 02-03 Summarize quantitative data using frequency distributions,
histograms, frequency polygons, and ogives.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
43
Copyright 2019 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior
written consent of McGraw-Hill Education.
7) When we wish to summarize the proportion (or fraction) of items in a class, we use the
frequency distribution for each class.
Answer: FALSE
Explanation: The relative frequency summarizes the proportion (or fraction) of items in a class.
Frequency distribution shows actual counts of items in each class.
Difficulty: 2 Medium
Topic: Graphically Summarizing Qualitative Data; Graphically Summarizing Quantitative Data
Learning Objective: 02-03 Summarize quantitative data using frequency distributions,
histograms, frequency polygons, and ogives.; 02-01 Summarize qualitative data by using
frequency distributions, bar charts, and pie charts.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
8) When establishing the classes for a frequency distribution, it is generally agreed that the more
classes you use the better your frequency distribution will be.
Answer: FALSE
Explanation: Classes should be determined by the number of data measurements.
Difficulty: 1 Easy
Topic: Graphically Summarizing Quantitative Data
Learning Objective: 02-03 Summarize quantitative data using frequency distributions,
histograms, frequency polygons, and ogives.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
9) The cumulative frequency for a class will always be at least as large as the cumulative
frequency for any class with a smaller upper boundary.
Answer: TRUE
Explanation: This is the number of measurements that are less than the upper boundary of the
class.
Difficulty: 2 Medium
Topic: Graphically Summarizing Quantitative Data
Learning Objective: 02-03 Summarize quantitative data using frequency distributions,
histograms, frequency polygons, and ogives.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
44
Copyright 2019 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior
written consent of McGraw-Hill Education.
10) A frequency table includes row and column percentages.
Answer: FALSE
Explanation: Frequency tables include frequencies, relative frequency, and percent frequency.
Cross-tabulation tables include row and column percentages.
Difficulty: 2 Medium
Topic: Graphically Summarizing Qualitative Data; Graphically Summarizing Quantitative Data
Learning Objective: 02-03 Summarize quantitative data using frequency distributions,
histograms, frequency polygons, and ogives.; 02-01 Summarize qualitative data by using
frequency distributions, bar charts, and pie charts.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
11) When constructing a graphical display that utilizes categorical data, classes that have
frequencies of 5 percent or less are usually combined together into a single category.
Answer: TRUE
Explanation: This is done so we can combine the categorical data in a way that is visually
pleasing to read and analyze.
Difficulty: 2 Medium
Topic: Graphically Summarizing Qualitative Data
Learning Objective: 02-02 Construct and interpret Pareto charts.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
12) In a Pareto chart, the bar for the "Other" category should be placed to the far left of the chart.
Answer: FALSE
Explanation: The bar to the far left of the Pareto chart will be the category with the highest
frequency.
Difficulty: 1 Easy
Topic: Graphically Summarizing Qualitative Data
Learning Objective: 02-02 Construct and interpret Pareto charts.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
45
Copyright 2019 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior
written consent of McGraw-Hill Education.
13) In the first step of setting up a Pareto chart, a frequency table should be constructed of the
defects (or categories) in decreasing order of frequency.
Answer: TRUE
Explanation: The defect with the highest frequency will be at the top of the table and so forth.
Difficulty: 2 Medium
Topic: Graphically Summarizing Qualitative Data
Learning Objective: 02-02 Construct and interpret Pareto charts.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
14) It is possible to create different interpretations of the same graphical display by simply using
different captions.
Answer: TRUE
Explanation: It is all in the way that the analyzer would like to display and depict the data to the
reader.
Difficulty: 2 Medium
Topic: Misleading Graphs and charts
Learning Objective: 02-08 Recognize misleading graphs and charts.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
15) Beginning the vertical scale of a graph at a value different from zero can cause increases to
look more dramatic.
Answer: TRUE
Explanation: This can cause extreme interpretations at first; it is always important to note on
your graph what value you are beginning with on your graph.
Difficulty: 2 Medium
Topic: Misleading Graphs and charts
Learning Objective: 02-08 Recognize misleading graphs and charts.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
46
Copyright 2019 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior
written consent of McGraw-Hill Education.
16) A runs plot is a form of scatter plot.
Answer: TRUE
Explanation: A runs plot is also known as a times series plot.
Difficulty: 1 Easy
Topic: Scatter Plots
Learning Objective: 02-07 Examine the relationships between variables by using scatter plots.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
17) The stem-and-leaf display is advantageous because it allows us to actually see the
measurements in the data set.
Answer: TRUE
Explanation: It visually displays all of the data points that were collected for an analysis.
Difficulty: 1 Easy
Topic: Stem-and-Leaf Displays
Learning Objective: 02-05 Construct and interpret stem-and-leaf displays.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
18) Splitting the stems refers to assigning the same stem to two or more rows of the stem-andleaf display.
Answer: TRUE
Explanation: This is another way of stretching the display of the data.
Difficulty: 2 Medium
Topic: Stem-and-Leaf Displays
Learning Objective: 02-05 Construct and interpret stem-and-leaf displays.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
19) When data are qualitative, the bars should never be separated by gaps.
Answer: FALSE
Explanation: Bar graphs for qualitative data are displayed with a gap between each category.
Difficulty: 2 Medium
Topic: Graphically Summarizing Qualitative Data
Learning Objective: 02-01 Summarize qualitative data by using frequency distributions, bar
charts, and pie charts.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
47
Copyright 2019 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior
written consent of McGraw-Hill Education.
20) Each stem of a stem-and-leaf display should be a single digit.
Answer: FALSE
Explanation: Leaves on the stem-and-leaf are a single digit.
Difficulty: 2 Medium
Topic: Stem-and-Leaf Displays
Learning Objective: 02-05 Construct and interpret stem-and-leaf displays.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
21) Leaves on a stem-and-leaf display should be rearranged so that they are in increasing order
from left to right.
Answer: TRUE
Explanation: This helps keeps order and aids in helping the reader to visually see all of the data.
Difficulty: 2 Medium
Topic: Stem-and-Leaf Displays
Learning Objective: 02-05 Construct and interpret stem-and-leaf displays.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
22) Gauges feature a single measure showing variation over time.
Answer: FALSE
Explanation: Sparklines feature a single measure showing variation over time.
Difficulty: 2 Medium
Topic: Graphical Descriptive Analytics
Learning Objective: 02-09 Construct and interpret gauges, bullet graphs, treemaps, and
sparklines.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
23) Data drill down is a form of data discovery.
Answer: TRUE
Explanation: Data drill down reveals more detailed data that underlie a higher-level summary.
Difficulty: 1 Easy
Topic: Graphical Descriptive Analytics
Learning Objective: 02-09 Construct and interpret gauges, bullet graphs, treemaps, and
sparklines.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
48
Copyright 2019 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior
written consent of McGraw-Hill Education.
24) Treemaps are used to compare multiple stem-and-leaf diagrams.
Answer: FALSE
Explanation: Treemaps help visualize two (or more) variables in a series of clustered rectangles.
Difficulty: 2 Medium
Topic: Graphical Descriptive Analytics
Learning Objective: 02-09 Construct and interpret gauges, bullet graphs, treemaps, and
sparklines.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
25) Sparklines always need to be displayed with either their axes or coordinates.
Answer: FALSE
Explanation: Sparklines seldom show their axes or coordinates.
Difficulty: 2 Medium
Topic: Graphical Descriptive Analytics
Learning Objective: 02-09 Construct and interpret gauges, bullet graphs, treemaps, and
sparklines.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
26) A bullet graph features a single measure and displays it as either a horizontal or vertical bar.
Answer: TRUE
Explanation: These ranges of the single measure represent qualitative measures of performance
and can be displayed as different colors of varying intensities.
Difficulty: 1 Easy
Topic: Graphical Descriptive Analytics
Learning Objective: 02-09 Construct and interpret gauges, bullet graphs, treemaps, and
sparklines.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
49
Copyright 2019 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior
written consent of McGraw-Hill Education.
27) Key performance indicators are best represented by a data discovery method.
Answer: FALSE
Explanation: KPIs are best represented by an analytic dashboard.
Difficulty: 3 Hard
Topic: Graphical Descriptive Analytics
Learning Objective: 02-09 Construct and interpret gauges, bullet graphs, treemaps, and
sparklines.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
28) A treemap displays information as a series of clustered rectangles.
Answer: TRUE
Explanation: This large rectangle in the treemap can be broken into smaller rectangles to
represent major segments.
Difficulty: 1 Easy
Topic: Graphical Descriptive Analytics
Learning Objective: 02-09 Construct and interpret gauges, bullet graphs, treemaps, and
sparklines.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
29) Sparklines are line charts and are often embedded with the text where they are being
discussed.
Answer: TRUE
Explanation: Sparklines represent the general shape of the variation in some measurement such
as temperature or price.
Difficulty: 2 Medium
Topic: Graphical Descriptive Analytics
Learning Objective: 02-09 Construct and interpret gauges, bullet graphs, treemaps, and
sparklines.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
50
Copyright 2019 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior
written consent of McGraw-Hill Education.
30) An analytic dashboard presents both current and historical trends of a business's key
performance indicators.
Answer: TRUE
Explanation: This allows the reader to monitor the key functions in a particular business.
Difficulty: 2 Medium
Topic: Graphical Descriptive Analytics
Learning Objective: 02-09 Construct and interpret gauges, bullet graphs, treemaps, and
sparklines.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
31) If space is an issue when presenting analytic dashboard graphics, gauges should be used most
frequently.
Answer: FALSE
Explanation: Gauges take up considerable space and are cluttered.
Difficulty: 3 Hard
Topic: Graphical Descriptive Analytics
Learning Objective: 02-09 Construct and interpret gauges, bullet graphs, treemaps, and
sparklines.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
32) Which of the following is not a graphical tool for descriptive analytics (dashboards)?
A) bullet graph
B) sparkline
C) raw data
D) treemap
E) gauge
Answer: C
Explanation: Raw data is data that has not been processed; no graphical tools have been applied
to it yet.
Difficulty: 1 Easy
Topic: Graphical Descriptive Analytics
Learning Objective: 02-09 Construct and interpret gauges, bullet graphs, treemaps, and
sparklines.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
51
Copyright 2019 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior
written consent of McGraw-Hill Education.
33) A(n) ________ is a graphical presentation of the current status and historical trends of a
business's key performance indicators.
A) frequency distribution
B) histogram
C) Pareto chart
D) dashboard
Answer: D
Explanation: A dashboard analysis allows you to monitor all of the key functions of a business.
Difficulty: 2 Medium
Topic: Graphical Descriptive Analytics
Learning Objective: 02-09 Construct and interpret gauges, bullet graphs, treemaps, and
sparklines.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
34) As a business owner, I have requested my staff to develop a set of dashboards that can be
used by the public to show wait time at each of my four local coffee shops at peak times during
the day and whether the time is short, medium, or long. Which of the following graphical
displays would be the best choice?
A) bullet graph
B) sparkline
C) treemap
D) gauges
Answer: A
Explanation: A bullet graph is used when you are analyzing a single measure—in this case wait
time.
Difficulty: 3 Hard
Topic: Graphical Descriptive Analytics
Learning Objective: 02-09 Construct and interpret gauges, bullet graphs, treemaps, and
sparklines.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
52
Copyright 2019 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior
written consent of McGraw-Hill Education.
35) Which of the following is the best analytic dashboard graphical method for visualizing
hierarchical information?
A) bullet graph
B) sparkline
C) treemap
D) gauge
Answer: C
Explanation: A treemap is used when visualizing hierarchical information because the
information is displayed as a tree where different branchings would be used to show the
hierarchical information.
Difficulty: 2 Medium
Topic: Graphical Descriptive Analytics
Learning Objective: 02-09 Construct and interpret gauges, bullet graphs, treemaps, and
sparklines.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
36) Which of the following tools used by graphical descriptive analytics will show variation over
time?
A) bullet graph
B) sparkline
C) treemap
D) gauge
Answer: B
Explanation: A sparkline is a line chart that presents the general shape of the variation in some
particular measures like temperature or price.
Difficulty: 2 Medium
Topic: Graphical Descriptive Analytics
Learning Objective: 02-09 Construct and interpret gauges, bullet graphs, treemaps, and
sparklines.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
53
Copyright 2019 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior
written consent of McGraw-Hill Education.
37) A(n) ________ is a graph of a cumulative distribution.
A) histogram
B) scatter plot
C) ogive
D) pie chart
Answer: C
Explanation: An ogive is a graph of the cumulative frequency of the class or the cumulative
relative frequencies or the cumulative percent frequencies.
Difficulty: 2 Medium
Topic: Graphically Summarizing Quantitative Data
Learning Objective: 02-03 Summarize quantitative data using frequency distributions,
histograms, frequency polygons, and ogives.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
38) ________ can be used to study the relationship between two variables.
A) Cross-tabulation tables
B) Frequency tables
C) Cumulative frequency distributions
D) Dot plots
Answer: A
Explanation: Frequency distributions and dot plots only use one variable. To study the
relationship between two variables, you need to use either cross-tabulation tables or scatter plots.
Difficulty: 1 Easy
Topic: Contingency Tables
Learning Objective: 02-06 Examine the relationships between variables by using contingency
tables.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
54
Copyright 2019 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior
written consent of McGraw-Hill Education.
39) Row or column percentages can be found in
A) frequency tables.
B) relative frequency tables.
C) cross-tabulation tables.
D) cumulative frequency tables.
Answer: C
Explanation: Cross-tabulation tables show the relationship between two variables using rows
and column percentages.
Difficulty: 2 Medium
Topic: Contingency Tables
Learning Objective: 02-06 Examine the relationships between variables by using contingency
tables.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
40) All of the following are used to describe quantitative data except the ________.
A) histogram
B) stem-and-leaf chart
C) dot plot
D) pie chart
Answer: D
Explanation: Pie charts are used only for categorical or qualitative data.
Difficulty: 2 Medium
Topic: Graphically Summarizing Quantitative Data
Learning Objective: 02-03 Summarize quantitative data using frequency distributions,
histograms, frequency polygons, and ogives.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
55
Copyright 2019 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior
written consent of McGraw-Hill Education.
41) An unusually large or small observation separated from the rest of the data is a(n) ________.
A) absolute extreme
B) outlier
C) mode
D) quartile
Answer: B
Explanation: Outliers are identified as measurements that are widely separated from the other
data measurements.
Difficulty: 1 Easy
Topic: Stem-and-Leaf Displays; Dot Plots
Learning Objective: 02-05 Construct and interpret stem-and-leaf displays.; 02-04 Construct and
interpret dot plots.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
42) Which of the following graphs is for qualitative data?
A) histogram
B) bar chart
C) ogive plot
D) stem-and-leaf
Answer: B
Explanation: Histogram, stem-and-leaf, and frequency (ogive) graphs display quantitative data.
Difficulty: 2 Medium
Topic: Graphically Summarizing Qualitative Data
Learning Objective: 02-01 Summarize qualitative data by using frequency distributions, bar
charts, and pie charts.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
56
Copyright 2019 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior
written consent of McGraw-Hill Education.
43) A plot that allows us to visualize the relationship between two variables is a(n) ________
plot.
A) frequency
B) scatter
C) dot
D) ogive
Answer: B
Explanation: Scatter plots display the relationship between two variables.
Difficulty: 2 Medium
Topic: Scatter Plots
Learning Objective: 02-07 Examine the relationships between variables by using scatter plots.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
44) A stem-and-leaf display is best used to ________.
A) provide a point estimate of the variability of the data set
B) provide a point estimate of the central tendency of the data set
C) display the shape of the distribution
D) display a two-variable treemap
Answer: C
Explanation: It is more difficult to find central tendency and variability using a stem-and-leaf
display. It is easy to visualize the shape of the distribution using stem-and-leaf.
Difficulty: 2 Medium
Topic: Stem-and-Leaf Displays
Learning Objective: 02-05 Construct and interpret stem-and-leaf displays.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
57
Copyright 2019 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior
written consent of McGraw-Hill Education.
45) Which of the following divides quantitative measurements into classes and graphs the
frequency, relative frequency, or percentage frequency for each class?
A) histogram
B) dot plot
C) stem-and-leaf display
D) scatter plot
Answer: A
Explanation: A box plot does not easily group measurements into classes; a scatter plot is for
looking at the relationship between two variables.
Difficulty: 3 Hard
Topic: Graphically Summarizing Quantitative Data
Learning Objective: 02-03 Summarize quantitative data using frequency distributions,
histograms, frequency polygons, and ogives.
Bloom's: Understand
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
46) A ________ displays the frequency of each class with qualitative data and a ________
displays the frequency of each class with quantitative data.
A) histogram; stem-and-leaf display
B) bar chart; histogram
C) scatter plot; bar chart
D) stem-and-leaf; pie chart
Answer: B
Explanation: The histogram and stem-and-leaf are used to graphically display quantitative data;
a scatter plot is used for displaying the relationship between two variables.
Difficulty: 2 Medium
Topic: Graphically Summarizing Qualitative Data; Graphically Summarizing Quantitative Data
Learning Objective: 02-03 Summarize quantitative data using frequency distributions,
histograms, frequency polygons, and ogives.; 02-01 Summarize qualitative data by using
frequency distributions, bar charts, and pie charts.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
58
Copyright 2019 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior
written consent of McGraw-Hill Education.
47) A ________ shows the relationship between two variables.
A) stem-and-leaf
B) bar chart
C) histogram
D) scatter plot
E) pie chart
Answer: D
Explanation: Pie charts and bar charts are used for a single qualitative variable; stem-and-leaf
charts and histograms are used for displaying a single quantitative variable.
Difficulty: 2 Medium
Topic: Scatter Plots
Learning Objective: 02-07 Examine the relationships between variables by using scatter plots.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
48) A(n) ________ can be used to differentiate the "vital few" causes of quality problems from
the "trivial many" causes of quality problems.
A) histogram
B) scatter plot
C) pareto chart
D) ogive plot
E) stem-and-leaf display
Answer: C
Explanation: A pareto chart is a specialized bar chart to look at the frequency of categories; a
scatter plot is for displaying the relationship between two variables; a histogram, stem-and-leaf,
and ogive plot are used to display quantitative data.
Difficulty: 2 Medium
Topic: Graphically Summarizing Qualitative Data
Learning Objective: 02-02 Construct and interpret Pareto charts.
Bloom's: Understand
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
59
Copyright 2019 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior
written consent of McGraw-Hill Education.
49) ________ and ________ are used to describe qualitative (categorical) data.
A) Stem-and-leaf displays; scatter plots
B) Scatter plots; histograms
C) Dot plots; bar charts
D) Bar charts; pie charts
E) Pie charts; histograms
Answer: D
Explanation: Stem-and-leaf displays, box plots, and histograms are used for quantitative data;
scatter plots are for displaying the relationship between two variables.
Difficulty: 2 Medium
Topic: Graphically Summarizing Qualitative Data
Learning Objective: 02-01 Summarize qualitative data by using frequency distributions, bar
charts, and pie charts.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
50) Which one of the following graphical tools is used with quantitative data?
A) bar chart
B) histogram
C) pie chart
D) Pareto chart
Answer: B
Explanation: Pie charts, Pareto charts, and bar charts are used with categorical/qualitative data.
Difficulty: 2 Medium
Topic: Graphically Summarizing Quantitative Data
Learning Objective: 02-03 Summarize quantitative data using frequency distributions,
histograms, frequency polygons, and ogives.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
60
Copyright 2019 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior
written consent of McGraw-Hill Education.
51) When developing a frequency distribution, the class (group) intervals must be ________.
A) large
B) small
C) integer
D) nonoverlapping
E) equal
Answer: D
Explanation: There is no definitive size of intervals for classes, and intervals can be fractional.
The number of classes can result in the final class having a different interval size than the
previous ones.
Difficulty: 3 Hard
Topic: Graphically Summarizing Quantitative Data
Learning Objective: 02-03 Summarize quantitative data using frequency distributions,
histograms, frequency polygons, and ogives.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
52) Which of the following graphical tools is not used to study the shapes of distributions?
A) stem-and-leaf display
B) scatter plot
C) histogram
D) dot plot
Answer: B
Explanation: Scatter plots are used to display the relationship between two variables.
Difficulty: 2 Medium
Topic: Graphically Summarizing Quantitative Data
Learning Objective: 02-03 Summarize quantitative data using frequency distributions,
histograms, frequency polygons, and ogives.
Bloom's: Understand
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
61
Copyright 2019 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior
written consent of McGraw-Hill Education.
53) All of the following are used to describe qualitative data except the ________.
A) bar chart
B) pie chart
C) histogram
D) Pareto chart
Answer: C
Explanation: Histograms are used for quantitative data.
Difficulty: 2 Medium
Topic: Graphically Summarizing Qualitative Data
Learning Objective: 02-01 Summarize qualitative data by using frequency distributions, bar
charts, and pie charts.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
54) If there are 130 values in a data set, how many classes should be created for a frequency
histogram?
A) 4
B) 5
C) 6
D) 7
E) 8
Answer: E
Explanation:
2k, where k = number of classes and 2k is the closest value larger than 130.
27 = 128; 28 = 256.
Difficulty: 2 Medium
Topic: Graphically Summarizing Quantitative Data
Learning Objective: 02-03 Summarize quantitative data using frequency distributions,
histograms, frequency polygons, and ogives.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
62
Copyright 2019 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior
written consent of McGraw-Hill Education.
55) If there are 120 values in a data set, how many classes should be created for a frequency
histogram?
A) 4
B) 5
C) 6
D) 7
E) 8
Answer: D
Explanation: 2k, where k = number of classes and 2k is the closest value larger than 120.
27 = 128.
Difficulty: 2 Medium
Topic: Graphically Summarizing Quantitative Data
Learning Objective: 02-03 Summarize quantitative data using frequency distributions,
histograms, frequency polygons, and ogives.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
56) If there are 62 values in a data set, how many classes should be created for a frequency
histogram?
A) 4
B) 5
C) 6
D) 7
E) 8
Answer: C
Explanation: 2k, where k = number of classes and 2k is the closest value larger than 62.
26 = 64.
Difficulty: 2 Medium
Topic: Graphically Summarizing Quantitative Data
Learning Objective: 02-03 Summarize quantitative data using frequency distributions,
histograms, frequency polygons, and ogives.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
63
Copyright 2019 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior
written consent of McGraw-Hill Education.
57) If there are 30 values in a data set, how many classes should be created for a frequency
histogram?
A) 4
B) 5
C) 6
D) 7
E) 8
Answer: B
Explanation: 2k, where k = number of classes and 2k is the closest value larger than 30.
25 = 32.
Difficulty: 2 Medium
Topic: Graphically Summarizing Quantitative Data
Learning Objective: 02-03 Summarize quantitative data using frequency distributions,
histograms, frequency polygons, and ogives.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
64
Copyright 2019 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior
written consent of McGraw-Hill Education.
58) A CFO is looking at what percentage of a company's resources are spent on computing. He
samples companies in the pharmaceutical industry and develops the following stem-and-leaf
display (leaf unit = 0.1).
5
6
7
8
9
10
11
12
13
269
255568999
11224557789
001222458
02455679
1556
137
255
What is the approximate shape of the distribution of the data?
A) normal
B) skewed to the right
C) skewed to the left
D) bimodal
E) uniform
Answer: B
Explanation: With outliers at the stem of 13 and the majority of the data grouped around stems
6, 7, and 8, the shape is skewed with the outliers to the right.
Difficulty: 2 Medium
Topic: Stem-and-Leaf Displays
Learning Objective: 02-05 Construct and interpret stem-and-leaf displays.
Bloom's: Analyze
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
65
Copyright 2019 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior
written consent of McGraw-Hill Education.
59) A CFO is looking at what percentage of a company's resources are spent on computing. He
samples companies in the pharmaceutical industry and develops the following stem-and-leaf
display (leaf unit = 0.1).
5
6
7
8
9
10
11
12
13
269
255568999
11224557789
001222458
02455679
1556
137
255
What is the smallest percentage spent on R&D?
A) 5.9
B) 5.6
C) 5.2
D) 5.02
E) 50.2
Answer: C
Explanation: The smallest value displayed in the graph is 5.2 percent.
Difficulty: 2 Medium
Topic: Stem-and-Leaf Displays
Learning Objective: 02-05 Construct and interpret stem-and-leaf displays.
Bloom's: Apply
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
66
Copyright 2019 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior
written consent of McGraw-Hill Education.
60) A CFO is looking at what percentage of a company's resources are spent on computing. He
samples companies in the pharmaceutical industry and develops the following stem-and-leaf
display (leaf unit = 0.1).
5
6
7
8
9
10
11
12
13
269
255568999
11224557789
001222458
02455679
1556
137
255
If you were creating a frequency histogram using these data, how many classes would you
create?
A) 4
B) 5
C) 6
D) 7
E) 8
Answer: C
Explanation: There are 50 data measurements. 2k, where k = number of classes and 2k is the
closest value larger than 50. 26 = 64.
Difficulty: 2 Medium
Topic: Stem-and-Leaf Displays; Graphically Summarizing Quantitative Data
Learning Objective: 02-05 Construct and interpret stem-and-leaf displays.; 02-03 Summarize
quantitative data using frequency distributions, histograms, frequency polygons, and ogives.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
67
Copyright 2019 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior
written consent of McGraw-Hill Education.
61) A CFO is looking at what percentage of a company's resources are spent on computing. He
samples companies in the pharmaceutical industry and develops the following stem-and-leaf
display (leaf unit = 0.1).
5
6
7
8
9
10
11
12
13
269
255568999
11224557789
001222458
02455679
1556
137
255
What would be the class length used in creating a frequency histogram?
A) 1.4
B) 8.3
C) 1.2
D) 1.7
E) 0.9
Answer: A
Explanation: There are 50 data measurements. 2k, where k = number of classes and 2k is the
closest value larger than 50. 26 = 64, so 6 classes. Class length = (Max value − Min value)/6 =
(13.5 − 5.2)/6. Length = 1.38, rounded to 1.4.
Difficulty: 2 Medium
Topic: Stem-and-Leaf Displays; Graphically Summarizing Quantitative Data
Learning Objective: 02-05 Construct and interpret stem-and-leaf displays.; 02-03 Summarize
quantitative data using frequency distributions, histograms, frequency polygons, and ogives.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
68
Copyright 2019 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior
written consent of McGraw-Hill Education.
62) A CFO is looking at what percentage of a company's resources are spent on computing. He
samples companies in the pharmaceutical industry and develops the following stem-and-leaf
display (leaf unit = 0.1).
5
6
7
8
9
10
11
12
13
269
255568999
11224557789
001222458
02455679
1556
137
255
What would be the first class interval for the frequency histogram?
A) 5.2 < 6.6
B) 5.2 < 6.0
C) 5.0 < 6.0
D) 5.0 < 6.4
E) 5.2 < 6.4
Answer: A
Explanation: There are 50 data measurements. 2k, where k = number of classes and 2k is the
closest value larger than 50. 26 = 64, so 6 classes. Class length = (Max value − Min value)/6 =
(13.5 − 5.2)/6. Length = 1.38, rounded to 1.4. The boundary for the first nonoverlapping interval
is the smallest measurement and the sum of the first measurement and the length (5.2 + 1.38 =
6.58). So the first interval will contain the values 5.2 − 6.5.
Difficulty: 2 Medium
Topic: Stem-and-Leaf Displays; Graphically Summarizing Quantitative Data
Learning Objective: 02-05 Construct and interpret stem-and-leaf displays.; 02-03 Summarize
quantitative data using frequency distributions, histograms, frequency polygons, and ogives.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
69
Copyright 2019 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior
written consent of McGraw-Hill Education.
63) A company's Chief Operating Officer (COO) keeps track of the mileage on her trips from her
office at corporate headquarters to the company's off-site manufacturing facility and its nearby
suppliers. The stem-and-leaf display of the data for one year is below.
76
77
78
79
80
81
82
83
9
114
07
88
2
1
88
How many trips were used in this display?
A) 7
B) 9
C) 10
D) 11
E) 12
Answer: E
Explanation: Count of measurements is 12.
Difficulty: 2 Medium
Topic: Stem-and-Leaf Displays
Learning Objective: 02-05 Construct and interpret stem-and-leaf displays.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
70
Copyright 2019 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior
written consent of McGraw-Hill Education.
64) A company's Chief Operating Officer (COO) keeps track of the mileage on her trips from her
office at corporate headquarters to the company's off-site manufacturing facility and its nearby
suppliers. The stem-and-leaf display of the data for one year is below.
76
77
78
79
80
81
82
83
9
114
07
88
2
1
88
In developing a histogram of these data, how many classes would be used?
A) 4
B) 5
C) 6
D) 7
E) 8
Answer: A
Explanation: Number of measurements = 12; 24 = 16; classes = 4.
Difficulty: 2 Medium
Topic: Stem-and-Leaf Displays; Graphically Summarizing Quantitative Data
Learning Objective: 02-05 Construct and interpret stem-and-leaf displays.; 02-03 Summarize
quantitative data using frequency distributions, histograms, frequency polygons, and ogives.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
71
Copyright 2019 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior
written consent of McGraw-Hill Education.
65) A company's Chief Operating Officer (COO) keeps track of the mileage on her trips from her
office at corporate headquarters to the company's off-site manufacturing facility and its nearby
suppliers. The stem-and-leaf display of the data for one year is below.
76
77
78
79
80
81
82
83
9
114
07
88
2
1
88
What would be the class length for creating the frequency histogram?
A) 14
B) 9
C) 27
D) 18
E) 23
Answer: D
Explanation:
Measurements = 12; classes = 4; class length = (838 − 769)/4 = 17.25, rounded to 18
Difficulty: 2 Medium
Topic: Stem-and-Leaf Displays; Graphically Summarizing Quantitative Data
Learning Objective: 02-05 Construct and interpret stem-and-leaf displays.; 02-03 Summarize
quantitative data using frequency distributions, histograms, frequency polygons, and ogives.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
72
Copyright 2019 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior
written consent of McGraw-Hill Education.
66) A company collected the ages from a random sample of its middle managers, with the
resulting frequency distribution shown below.
Class
Interval
20 to < 25
25 to < 30
30 to < 35
35 to < 40
40 to < 45
45 to < 50
Frequency
8
6
5
12
15
7
What would be the approximate shape of the relative frequency histogram?
A) symmetrical
B) uniform
C) linear
D) skewed to the left
E) skewed to the right
Answer: D
Explanation: The majority of data lie to the right side of the distribution; the tail of the smaller
number of measurements extends to the left, so the graph is skewed with a tail to the left.
Difficulty: 2 Medium
Topic: Graphically Summarizing Quantitative Data
Learning Objective: 02-03 Summarize quantitative data using frequency distributions,
histograms, frequency polygons, and ogives.
Bloom's: Understand
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
73
Copyright 2019 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior
written consent of McGraw-Hill Education.
67) A company collected the ages from a random sample of its middle managers, with the
resulting frequency distribution shown below.
Class
Interval
20 to < 25
25 to < 30
30 to < 35
35 to < 40
40 to < 45
45 to < 50
Frequency
8
6
5
12
15
7
What is the relative frequency for the class with the greatest frequency?
A) .132
B) .226
C) .231
D) .283
E) .288
Answer: D
Explanation: Measurements = 53; largest interval has 15 measurements.15/53 = .283.
Difficulty: 3 Hard
Topic: Graphically Summarizing Quantitative Data
Learning Objective: 02-03 Summarize quantitative data using frequency distributions,
histograms, frequency polygons, and ogives.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
74
Copyright 2019 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior
written consent of McGraw-Hill Education.
68) A company collected the ages from a random sample of its middle managers, with the
resulting frequency distribution shown below.
Class
Interval
20 to < 25
25 to < 30
30 to < 35
35 to < 40
40 to < 45
45 to < 50
Frequency
8
6
5
12
15
7
What is the midpoint of the third class interval?
A) 22.5
B) 27.5
C) 32.5
D) 37.5
E) 42.5
Answer: C
Explanation: The midpoint is calculated as halfway between the boundaries of the class. The
third class interval is 30 to 35, which yields a midpoint of 32.5.
Difficulty: 3 Hard
Topic: Graphically Summarizing Quantitative Data
Learning Objective: 02-03 Summarize quantitative data using frequency distributions,
histograms, frequency polygons, and ogives.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
75
Copyright 2019 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior
written consent of McGraw-Hill Education.
69) The general term for a graphical display of categorical data made up of vertical or horizontal
bars is called a(n) ________.
A) pie chart
B) Pareto chart
C) bar chart
D) ogive plot
Answer: C
Explanation: An ogive plot is based on quantitative data, a Pareto chart is a specialized bar
chart, and a pie chart is a circular graphical display.
Difficulty: 2 Medium
Topic: Graphically Summarizing Qualitative Data
Learning Objective: 02-01 Summarize qualitative data by using frequency distributions, bar
charts, and pie charts.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
70) Pareto charts are frequently used to identify ________.
A) random data
B) the most common types of defects
C) outliers that do not show up on a dot plot
D) the cause for extreme skewness to the right
Answer: B
Explanation: By definition, a defect is a flaw in a population or sample element.
Difficulty: 2 Medium
Topic: Graphically Summarizing Qualitative Data
Learning Objective: 02-02 Construct and interpret Pareto charts.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
76
Copyright 2019 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior
written consent of McGraw-Hill Education.
71) A graphical portrayal of a quantitative data set that divides the data into classes and gives the
frequency of each class is a(n) ________.
A) ogive plot
B) dot plot
C) histogram
D) Pareto chart
E) bar chart
Answer: C
Explanation: Pareto and bar charts are used for qualitative data, a dot plot displays individual
data points, and an ogive plot is a curved display of the cumulative distribution of the data.
Difficulty: 2 Medium
Topic: Graphically Summarizing Quantitative Data
Learning Objective: 02-03 Summarize quantitative data using frequency distributions,
histograms, frequency polygons, and ogives.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
72) The number of measurements falling within a class interval is called the ________.
A) frequency
B) relative frequency
C) leaf
D) cumulative sum
Answer: A
Explanation: By definition, frequency is the number of measurements. Relative frequency is
proportional. A leaf is not a count but part of a graphical display, and the cumulative sum is not a
count.
Difficulty: 2 Medium
Topic: Graphically Summarizing Quantitative Data
Learning Objective: 02-03 Summarize quantitative data using frequency distributions,
histograms, frequency polygons, and ogives.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
77
Copyright 2019 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior
written consent of McGraw-Hill Education.
73) A relative frequency histogram having a longer tail to the right than to the left is said to be
________.
A) skewed to the left
B) normal
C) a scatter plot
D) skewed to the right
Answer: D
Explanation: A scatter plot is a graphical display of the relationship between two variables; a
normal curve is bell-shaped with even distribution on both sides of the high point of the curve.
The long tail direction defines the skewness of the graph, in this case skewed to the right.
Difficulty: 2 Medium
Topic: Graphically Summarizing Quantitative Data
Learning Objective: 02-03 Summarize quantitative data using frequency distributions,
histograms, frequency polygons, and ogives.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
74) The proportion of measurements in a class is called the ________ of that class.
A) frequency
B) relative frequency
C) leaf
D) cumulative percentage
Answer: B
Explanation: By definition, frequency is the number of measurements. Relative frequency is
proportional. A leaf and the cumulative sum are not counts of measurements or percentages.
Difficulty: 2 Medium
Topic: Graphically Summarizing Quantitative Data
Learning Objective: 02-03 Summarize quantitative data using frequency distributions,
histograms, frequency polygons, and ogives.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
78
Copyright 2019 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior
written consent of McGraw-Hill Education.
75) A histogram that has a longer tail extending toward larger values is ________.
A) skewed to the left
B) normal
C) a scatter plot
D) skewed to the right
Answer: D
Explanation: Larger values are to the right of the center part of the graph, resulting in a tail to
the right. Thus, the graph is skewed to the right.
Difficulty: 2 Medium
Topic: Graphically Summarizing Quantitative Data
Learning Objective: 02-03 Summarize quantitative data using frequency distributions,
histograms, frequency polygons, and ogives.
Bloom's: Understand
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
76) A histogram that has a longer tail extending toward smaller values is ________.
A) skewed to the left
B) normal
C) a scatter plot
D) skewed to the right
Answer: A
Explanation: Smaller values are to the left of the center part of the graph, resulting in a tail to the
left. Thus, the graph is skewed to the left.
Difficulty: 2 Medium
Topic: Graphically Summarizing Quantitative Data
Learning Objective: 02-03 Summarize quantitative data using frequency distributions,
histograms, frequency polygons, and ogives.
Bloom's: Understand
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
79
Copyright 2019 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior
written consent of McGraw-Hill Education.
77) A type of very simple graph that can be used to summarize a quantitative data set is a(n)
________.
A) runs plot
B) ogive plot
C) dot plot
D) pie chart
Answer: C
Explanation: A runs plot is used for time series data; a pie chart is used for qualitative data; an
ogive plot is a specialized graph of the cumulative distribution of data measurements. A dot plot
is a simple graphical display of data measurements.
Difficulty: 2 Medium
Topic: Dot Plots
Learning Objective: 02-04 Construct and interpret dot plots.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
78) An example of manipulating a graphical display to distort reality is ________.
A) starting the axes at zero
B) making the bars in a histogram equal widths
C) stretching the axes
D) adding an unbiased caption
Answer: C
Explanation: Starting the axes at zero is the appropriate method of graphical display, as is
making the bars in a histogram equal widths.
Difficulty: 2 Medium
Topic: Misleading Graphs and charts
Learning Objective: 02-08 Recognize misleading graphs and charts.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
80
Copyright 2019 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior
written consent of McGraw-Hill Education.
79) As a general rule, when creating a stem-and-leaf display, there should be ________ stem
values.
A) between 3 and 10
B) between 1 and 100
C) no fewer than 20
D) between 5 and 20
Answer: D
Explanation: By definition, there should be between 5 and 20 stems to enable a reasonable
display of the shape of the distribution.
Difficulty: 2 Medium
Topic: Stem-and-Leaf Displays
Learning Objective: 02-05 Construct and interpret stem-and-leaf displays.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
81
Copyright 2019 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior
written consent of McGraw-Hill Education.
80) At the end of their final exam, 550 students answered an additional question in which they
rated their instructor's teaching effectiveness, with the following results.
Student's Rating of Instructor
Very or Somewhat
Student's Final Grade
Effective
A
190
B
75
C
20
D
9
F
1
Very or Somewhat
Ineffective
85
120
17
18
15
What proportion of the students who rated their instructor as very or somewhat effective received
a B or better in the class?
A) 0.345
B) 0.254
C) 0.482
D) 0.898
E) 0.644
Answer: D
Explanation: 295 students rated their instructor as very or somewhat effective; (75 + 190) = 265
had a B or better; 265/295 = .898.
Difficulty: 3 Hard
Topic: Contingency Tables
Learning Objective: 02-06 Examine the relationships between variables by using contingency
tables.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
82
Copyright 2019 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior
written consent of McGraw-Hill Education.
81) At the end of their final exam, 550 students answered an additional question in which they
rated their instructor's teaching effectiveness, with the following results.
Student's Rating of Instructor
Very or Somewhat
Student's Final Grade
Effective
A
190
B
75
C
20
D
9
F
1
Very or Somewhat
Ineffective
85
120
17
18
15
What proportion of the students who rated their instructor as very or somewhat effective received
a C or lower in the class?
A) 0.03
B) 0.06
C) 0.10
D) 0.13
E) 0.15
Answer: C
Explanation: 295 received a C or lower in the class; 30/295 = 0.10.
Difficulty: 3 Hard
Topic: Contingency Tables
Learning Objective: 02-06 Examine the relationships between variables by using contingency
tables.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
83
Copyright 2019 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior
written consent of McGraw-Hill Education.
82) 822 recently purchased books were randomly selected from all recent book purchases over
the Internet. The chart below shows the breakdown of the classification of the book type.
What percentage of the books in the sample were either mystery or science fiction/fantasy?
A) 18.61
B) 36.50
C) 17.88
D) 24.33
E) 22.99
Answer: B
Explanation: 300 mystery or science fiction/fantasy books purchased; 300/822 = 36.5%.
Difficulty: 2 Medium
Topic: Graphically Summarizing Qualitative Data
Learning Objective: 02-01 Summarize qualitative data by using frequency distributions, bar
charts, and pie charts.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
84
Copyright 2019 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior
written consent of McGraw-Hill Education.
83) 822 recently purchased books were randomly selected from all recent book purchases over
the Internet. The chart below shows the breakdown of the classification of the book type.
What percentage of the books in the sample were self-help books?
A) 11.44
B) .1144
C) 1.82
D) 0.0182
E) 0.940
Answer: A
Explanation: 94/822 = 11.44%
Difficulty: 2 Medium
Topic: Graphically Summarizing Qualitative Data
Learning Objective: 02-01 Summarize qualitative data by using frequency distributions, bar
charts, and pie charts.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
85
Copyright 2019 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior
written consent of McGraw-Hill Education.
84) 822 recently purchased books were randomly selected from all recent book purchases over
the Internet. The chart below shows the breakdown of the classification of the book type.
What percentage of the books in the sample were in the top two categories?
A) 22.99
B) 20.44
C) 4.50
D) 43.43
E) 0.4343
Answer: D
Explanation:
189 + 168 = 357 in the top two categories; 357/822 = 43.43% of the total purchased.
Difficulty: 2 Medium
Topic: Graphically Summarizing Qualitative Data
Learning Objective: 02-01 Summarize qualitative data by using frequency distributions, bar
charts, and pie charts.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
86
Copyright 2019 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior
written consent of McGraw-Hill Education.
85) Using the following data, describe the shape of the data distribution.
1.
2.
3.
4.
5.
11.5
13.5
12.5
15.2
14.7
6.
7.
8.
9.
10.
13.7
14.0
12.0
12.7
12.5
11.
12.
13.
14.
15.
11.0
13.0
16.7
12.5
11.5
16.
17.
18.
19.
20.
14.5
15.5
13.0
18.2
11.7
A) skewed to the left
B) bimodal
C) normal
D) skewed to the right
Answer: D
Explanation: Create a stem-and-leaf graph. The stem would be 11,12,13,14,15,16,17,18; leaves
would be the tenth on each data measurement:
The graphical display shows that it is skewed to the right.
Difficulty: 2 Medium
Topic: Graphically Summarizing Qualitative Data
Learning Objective: 02-03 Summarize quantitative data using frequency distributions,
histograms, frequency polygons, and ogives.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
87
Copyright 2019 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior
written consent of McGraw-Hill Education.
86) Using the following data, what would be the range of the values of the stem in a stem-andleaf display?
1.
2.
3.
4.
5.
11.5
13.5
12.5
15.2
14.7
6.
7.
8.
9.
10.
13.7
14.0
12.0
12.7
12.5
11.
12.
13.
14.
15.
11.0
13.0
16.7
12.5
11.5
16.
17.
18.
19.
20.
14.5
15.5
13.0
18.2
11.7
A) 11-17
B) 11-18
C) 10-18
D) 12-17
E) 12-18
Answer: B
Explanation: Create a stem-and-leaf graph. The stem would be 11,12,13,14,15,16,17,18; leaves
would be the tenth on each data measurement:
Difficulty: 2 Medium
Topic: Stem-and-Leaf Displays
Learning Objective: 02-05 Construct and interpret stem-and-leaf displays.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
88
Copyright 2019 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior
written consent of McGraw-Hill Education.
87) Using the following data, what would be the leaf unit in a stem-and-leaf display?
1.
2.
3.
4.
5.
11.5
13.5
12.5
15.2
14.7
6.
7.
8.
9.
10.
13.7
14.0
12.0
12.7
12.5
11.
12.
13.
14.
15.
11.0
13.0
16.7
12.5
11.5
16.
17.
18.
19.
20.
14.5
15.5
13.0
18.2
11.7
A) 1.0
B) 10
C) .10
D) .01
E) .20
Answer: C
Explanation: Create a stem-and-leaf graph. The stem would be 11,12,13,14,15,16,17,18; leaves
would be the tenth on each data measurement.
Difficulty: 2 Medium
Topic: Stem-and-Leaf Displays
Learning Objective: 02-05 Construct and interpret stem-and-leaf displays.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
89
Copyright 2019 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior
written consent of McGraw-Hill Education.
88) Consider the following data on distances traveled by people to visit the local amusement
park and calculate the relative frequency for the shortest distance.
Distance
1-8 miles
9-16 miles
17-24 miles
25-32 miles
33-40 miles
Frequency
15
12
7
5
1
A) .375
B) .150
C) .500
D) .300
E) .333
Answer: A
Explanation: Total of 40 measurements: 15/40 = .375.
Difficulty: 1 Easy
Topic: Graphically Summarizing Quantitative Data
Learning Objective: 02-03 Summarize quantitative data using frequency distributions,
histograms, frequency polygons, and ogives.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
90
Copyright 2019 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior
written consent of McGraw-Hill Education.
89) Consider the following data on distances traveled by people to visit the local amusement
park and calculate the relative frequency for the distances over 24 miles.
Distance
1-8 miles
9-16 miles
17-24 miles
25-32 miles
33-40 miles
Frequency
15
12
7
5
1
A) .375
B) .150
C) .125
D) .025
E) .325
Answer: B
Explanation: (5 + 1) = 6 over 24 miles; 6/40 = .15.
Difficulty: 2 Medium
Topic: Graphically Summarizing Quantitative Data
Learning Objective: 02-03 Summarize quantitative data using frequency distributions,
histograms, frequency polygons, and ogives.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
91
Copyright 2019 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior
written consent of McGraw-Hill Education.
90) The following is a partial relative frequency distribution of grades in an introductory
statistics course.
Grade
A
B
C
D
F
Relative
Frequency
0.22
?
0.18
0.17
0.06
Find the relative frequency for the B grade.
A) .78
B) .27
C) .65
D) .37
E) .47
Answer: D
Explanation: 1.00 − (.22 + .18 + .17 + .06) = 1.00 − .63 = .37
Difficulty: 1 Easy
Topic: Graphically Summarizing Qualitative Data
Learning Objective: 02-01 Summarize qualitative data by using frequency distributions, bar
charts, and pie charts.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
92
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written consent of McGraw-Hill Education.
91) The following is a relative frequency distribution of grades in an introductory statistics
course.
Grade
A
B
C
D
F
Relative
Frequency
0.22
?
0.18
0.17
0.06
If this was the distribution of 200 students, find the frequency for the highest two grades.
A) 44
B) 118
C) 59
D) 74
E) 35
Answer: B
Explanation: (.22 + .37) = .59. 59% of 200 = 118.
Difficulty: 2 Medium
Topic: Graphically Summarizing Qualitative Data
Learning Objective: 02-01 Summarize qualitative data by using frequency distributions, bar
charts, and pie charts.
Bloom's: Apply
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93
Copyright 2019 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior
written consent of McGraw-Hill Education.
92) The following is a relative frequency distribution of grades in an introductory statistics
course.
Grade
A
B
C
D
F
Relative
Frequency
0.22
?
0.18
0.17
0.06
If this was the distribution of 200 students, find the frequency of failures.
A) 12
B) 6
C) 23
D) 46
E) 3
Answer: A
Explanation: The frequency is .06. The frequency of failures is 6% of 200 = 12.
Difficulty: 2 Medium
Topic: Graphically Summarizing Qualitative Data
Learning Objective: 02-01 Summarize qualitative data by using frequency distributions, bar
charts, and pie charts.
Bloom's: Apply
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94
Copyright 2019 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior
written consent of McGraw-Hill Education.
93) The following is a relative frequency distribution of grades in an introductory statistics
course.
Grade
A
B
C
D
F
Relative
Frequency
0.22
?
0.18
0.17
0.06
If we wish to depict these data using a pie chart, find how many degrees should be assigned to
the highest grade of A.
A) 61.1
B) 22.0
C) 79.2
D) 90.0
E) 212.40
Answer: C
Explanation: A's are 22% of total; 360° in a circle: 22% of 360 = 79.2°.
Difficulty: 3 Hard
Topic: Graphically Summarizing Qualitative Data
Learning Objective: 02-01 Summarize qualitative data by using frequency distributions, bar
charts, and pie charts.
Bloom's: Apply
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95
Copyright 2019 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior
written consent of McGraw-Hill Education.
94) Recently an advertising company called 200 people and asked them to identify the company
that was in an ad running nationwide. The following results were obtained.
Correctly recalled the company
Incorrectly recalled the company
Total
Female
66
44
110
Male
50
40
90
Total
116
84
200
What percentage of those surveyed were female and could not recall the company?
A) 40.0
B) 22.0
C) 52.4
D) 66.7
E) 37.9
Answer: B
Explanation:
Out of 200 people, 44 were female and could not recall the company; 44/200 = 22%.
Difficulty: 2 Medium
Topic: Contingency Tables
Learning Objective: 02-06 Examine the relationships between variables by using contingency
tables.
Bloom's: Apply
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96
Copyright 2019 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior
written consent of McGraw-Hill Education.
95) Recently an advertising company called 200 people and asked them to identify the company
that was in an ad running nationwide. The following results were obtained.
Correctly recalled the company
Incorrectly recalled the company
Total
Female
66
44
110
Male
50
40
90
Total
116
84
200
What percentage of those surveyed could not correctly recall the company?
A) 58.00
B) 56.89
C) 55.00
D) 43.10
E) 42.00
Answer: E
Explanation: 84 of 200 could not recall the company; 84/200 = 42%.
Difficulty: 2 Medium
Topic: Contingency Tables
Learning Objective: 02-06 Examine the relationships between variables by using contingency
tables.
Bloom's: Apply
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97
Copyright 2019 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior
written consent of McGraw-Hill Education.
96) A local electronics retailer recently conducted a study on purchasers of large screen
televisions. The study recorded the type of television and the credit account balance of the
customer at the time of purchase. They obtained the following results.
Credit Balance
Under $200
$200 − $800
Over $800
Total
LED
10
8
16
34
LCD
16
12
12
40
Plasma
40
24
16
80
Projection
5
15
30
50
What percentage of purchases were plasma televisions by customers with the smallest credit
balances?
A) 50.0
B) 39.2
C) 56.3
D) 34.8
E) 19.6
Answer: E
Explanation: 40 of 204 total purchases; 40/204 = 19.6%
Difficulty: 2 Medium
Topic: Contingency Tables
Learning Objective: 02-06 Examine the relationships between variables by using contingency
tables.
Bloom's: Apply
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98
Copyright 2019 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior
written consent of McGraw-Hill Education.
97) A local electronics retailer recently conducted a study on purchasers of large screen
televisions. The study recorded the type of television and the credit account balance of the
customer at the time of purchase. They obtained the following results.
Credit Balance
Under $200
$200 − $800
Over $800
Total
LED
10
8
16
34
LCD
16
12
12
40
Plasma
40
24
16
80
Projection
5
15
30
50
What percentage of the customers had the highest credit balances and purchased an LCD
television?
A) 36.3
B) 5.9
C) 19.6
D) 56.3
E) 16.2
Answer: B
Explanation: 12 out of 204 = 5.9%.
Difficulty: 2 Medium
Topic: Contingency Tables
Learning Objective: 02-06 Examine the relationships between variables by using contingency
tables.
Bloom's: Apply
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99
Copyright 2019 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior
written consent of McGraw-Hill Education.
98) The number of weekly sales calls by a sample of 25 pharmaceutical salespersons is below.
24, 56, 43, 35, 37, 27, 29, 44, 34, 28, 33, 28, 46, 31, 38, 41, 48, 38, 27, 29, 37, 33, 31, 40, 50
How many classes should be used in the construction of a histogram?
A) 4
B) 6
C) 10
D) 5
E) 2
Answer: D
Explanation: Classes are determined by the value of k, where 2k yields a value that is closest to
the sample size and is also larger than the sample size.
k = 5, so 25 = 32.
Difficulty: 2 Medium
Topic: Graphically Summarizing Quantitative Data
Learning Objective: 02-03 Summarize quantitative data using frequency distributions,
histograms, frequency polygons, and ogives.
Bloom's: Apply
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100
Copyright 2019 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior
written consent of McGraw-Hill Education.
99) The number of weekly sales calls by a sample of 25 pharmaceutical salespersons is below.
24, 56, 43, 35, 37, 27, 29, 44, 34, 28, 33, 28, 46, 31, 38, 41, 48, 38, 27, 29, 37, 33, 31, 40, 50
What is the shape of the distribution of the data?
A) skewed to the right
B) skewed to the left
C) normal
D) bimodal
Answer: A
Explanation: Create a frequency table that can be used to observe the shape of the distribution.
Difficulty: 2 Medium
Topic: Graphically Summarizing Qualitative Data
Learning Objective: 02-03 Summarize quantitative data using frequency distributions,
histograms, frequency polygons, and ogives.
Bloom's: Apply
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101
Copyright 2019 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior
written consent of McGraw-Hill Education.
100) The number of items rejected daily by a manufacturer because of defects for the last 30
days are:
20, 21, 8, 17, 22, 19, 18, 19, 14, 17, 11, 6, 21, 25, 4, 19, 9, 12, 16, 16, 10, 28, 24, 6, 21, 20, 25, 5,
17, 8
How many classes should be used in constructing a histogram?
A) 6
B) 5
C) 7
D) 4
E) 8
Answer: B
Explanation: Number of classes = k, where 2k > 30. So k = 5.
Difficulty: 2 Medium
Topic: Graphically Summarizing Quantitative Data
Learning Objective: 02-03 Summarize quantitative data using frequency distributions,
histograms, frequency polygons, and ogives.
Bloom's: Apply
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102
Copyright 2019 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior
written consent of McGraw-Hill Education.
101) The number of weekly sales calls by a sample of 25 pharmaceutical salespersons is below.
24, 56, 43, 35, 37, 27, 29, 44, 34, 28, 33, 28, 46, 31, 38, 41, 48, 38, 27, 29, 37, 33, 31, 40, 50
Construct an ogive of the weekly sales calls.
Answer:
Create a frequency table with cumulative relative frequency and then construct the graph using
the cumulative frequency points.
Classes
Frequency
Rel Freq
24 < 31
31 < 38
38 < 45
45 < 52
52 < 57
7
8
6
3
1
0.28
0.32
0.24
0.12
0.04
Cum
Rel Freq
0.28
0.60
0.84
0.96
1.00
Difficulty: 3 Hard
Topic: Graphically Summarizing Quantitative Data
Learning Objective: 02-03 Summarize quantitative data using frequency distributions,
histograms, frequency polygons, and ogives.
Bloom's: Apply
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103
Copyright 2019 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior
written consent of McGraw-Hill Education.
102) The number of items rejected daily by a manufacturer because of defects for the last 30
days are:
20, 21, 8, 17, 22, 19, 18, 19, 14, 17, 11, 6, 21, 25, 4, 19, 9, 12, 16, 16, 10, 28, 24, 6, 21, 20, 25, 5,
17, 8
Complete this frequency table for these data.
Frequency
Rel Freq
Cum Freq
4<9
9 < 14
14 < 19
19 < 24
24 < 29
Answer:
Classes
Frequency
Rel Freq
4<9
9 < 14
14 < 19
19 < 24
24 < 29
6
4
7
9
4
0.2
0.133
0.233
0.30
0.133
Cum
Rel Freq
0.2
0.333
0.567
0.867
1.00
The Cum Freq column should be .566, .866, and 0.999. The values listed do not add to 1.00
exactly due to rounding.
Using the given classes, frequency = number of rejected items in each class, relative frequency =
frequency/30, and cumulative frequency = sum of successive class relative frequencies.
Difficulty: 2 Medium
Topic: Graphically Summarizing Quantitative Data
Learning Objective: 02-03 Summarize quantitative data using frequency distributions,
histograms, frequency polygons, and ogives.
Bloom's: Apply
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104
Copyright 2019 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior
written consent of McGraw-Hill Education.
103) The number of items rejected daily by a manufacturer because of defects for the last 30
days are:
20, 21, 8, 17, 22, 19, 18, 19, 14, 17, 11, 6, 21, 25, 4, 19, 9, 12, 16, 16, 10, 28, 24, 6, 21, 20, 25, 5,
17, 8
Construct a stem-and-leaf display.
Answer: One possible stem-and-leaf display (with each stem split into five):
Stem
0
0
0
1
1
1
1
1
2
2
2
2
2
Leaf
45
66
889
01
2
4
66777
8999
00111
2
455
8
A second possible stem-and-leaf display (with each stem split into two):
Stem
0
0
1
1
2
2
Leaf
4
566889
0124
66777899
0011124
558
Stem should be the 10s unit. Construct by splitting stems, since the range of values is only 5-28
and there should be approximately 10 stems. When splitting the stem, consider the number of
values in the split stems. Leaf unit should be the ones unit.
Difficulty: 2 Medium
Topic: Stem-and-Leaf Displays
Learning Objective: 02-05 Construct and interpret stem-and-leaf displays.
Bloom's: Apply
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105
Copyright 2019 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior
written consent of McGraw-Hill Education.
104) The number of items rejected daily by a manufacturer because of defects for the last 30
days are:
20, 21, 8, 17, 22, 19, 18, 19, 14, 17, 11, 6, 21, 25, 4, 19, 9, 12, 16, 16, 10, 28, 24, 6, 21, 20, 25, 5,
17, 8
Construct an ogive of the number of items rejected daily.
Answer:
Construct a frequency table (5 classes) with cumulative relative frequency.
Classes
Frequency
Rel Freq
4<9
9 < 14
14 < 19
19 < 24
24 < 29
6
4
7
9
4
0.20
0.13
0.23
0.30
0.13
Cum
Rel Freq
0.20
0.33
0.57
0.87
1.00
Difficulty: 2 Medium
Topic: Graphically Summarizing Quantitative Data
Learning Objective: 02-03 Summarize quantitative data using frequency distributions,
histograms, frequency polygons, and ogives.
Bloom's: Apply
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106
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written consent of McGraw-Hill Education.
105) Consider the following data.
1.
2.
3.
4.
5.
11.5
13.5
12.5
15.2
14.7
6.
7.
8.
9.
10.
13.7
14.0
12.0
12.7
12.5
11.
12.
13.
14.
15.
11.0
13.0
16.7
12.5
11.5
16.
17.
18.
19.
20.
14.5
15.5
13.0
18.2
11.7
Create a stem-and-leaf display for the sample.
Answer: One possible stem-and-leaf display as might be created by Minitab:
Stem-and-leaf of given data, N = 20, Leaf Unit = 0.10
4
9
(4)
7
4
2
1
1
11
12
13
14
15
16
17
18
0557
05557
0057
057
25
7
2
Stems should be from 11 to 18; leaves are the tenth unit.
Difficulty: 2 Medium
Topic: Stem-and-Leaf Displays
Learning Objective: 02-05 Construct and interpret stem-and-leaf displays.
Bloom's: Apply
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107
Copyright 2019 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior
written consent of McGraw-Hill Education.
106) Consider the following data on distances traveled by people to visit the local amusement
park.
Distance
1-8 miles
9-16 miles
17-24 miles
25-32 miles
33-40 miles
Frequency
15
12
7
5
1
Construct an ogive that corresponds to the frequency table.
Answer:
Calculate the relative frequency for each class (15/40, 12/40, 7/40, 5/40, 1/40; or .375, .30, .175,
.125, and .025) and then the cumulative frequency (.375, .675, .850, .975, 1.00).
Difficulty: 2 Medium
Topic: Graphically Summarizing Quantitative Data
Learning Objective: 02-03 Summarize quantitative data using frequency distributions,
histograms, frequency polygons, and ogives.
Bloom's: Apply
AACSB: Analytical Thinking
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108
Copyright 2019 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior
written consent of McGraw-Hill Education.
107) The following is a relative frequency distribution of grades in an introductory statistics
course.
Grade
A
B
C
D
F
Relative
Frequency
0.22
0.37
0.18
0.17
0.06
If this was the distribution of 200 students, give the frequency distribution for this data.
Answer:
Grade
A
B
C
D
F
Relative
Frequency
44
74
36
34
12
Convert from proportion (relative frequency) to frequency by multiplying each relative
frequency by 200 (e.g., .22 × 200 = 44 for grade A).
Difficulty: 2 Medium
Topic: Graphically Summarizing Quantitative Data
Learning Objective: 02-01 Summarize qualitative data by using frequency distributions, bar
charts, and pie charts.
Bloom's: Apply
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109
Copyright 2019 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior
written consent of McGraw-Hill Education.
108) The following is a relative frequency distribution of grades in an introductory statistics
course.
Grade
A
B
C
D
F
Relative
Frequency
0.22
0.37
0.18
0.17
0.06
Construct a percent bar chart for this data.
Answer:
Each grade category is displayed as a bar on a percent bar chart.
Difficulty: 1 Easy
Topic: Graphically Summarizing Qualitative Data
Learning Objective: 02-01 Summarize qualitative data by using frequency distributions, bar
charts, and pie charts.
Bloom's: Apply
AACSB: Analytical Thinking
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110
Copyright 2019 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior
written consent of McGraw-Hill Education.
109) The following is a relative frequency distribution of grades in an introductory statistics
course.
Grade
A
B
C
D
F
Relative
Frequency
0.22
0.37
0.18
0.17
0.06
If we wish to depict these data using a pie chart, find how many degrees (out of 360 degrees)
should be assigned to each grade.
Answer:
Grade
A
B
C
D
F
Relative
Frequency
79.2
133.2
64.8
61.2
21.6
Each proportion (relative frequency) is considered that portion of a circle's 360 degrees. Multiply
the relative frequency (proportion) by 360 to convert to actual circle degrees (e.g., grade A: .22 ×
360 = 79.2 degrees).
Difficulty: 2 Medium
Topic: Graphically Summarizing Qualitative Data
Learning Objective: 02-01 Summarize qualitative data by using frequency distributions, bar
charts, and pie charts.
Bloom's: Apply
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111
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written consent of McGraw-Hill Education.
110) Fill in the missing components of the following frequency distribution constructed for a
sample size of 50.
Class
Frequency
___ < 7.95
___ < 8.05
8.05 < ___
___ < 8.25
8.25 < ___
Rel Frequency
Cum
Rel Freq
0.12
0.48
0.24
0.10
Answer:
Class
Frequency
7.85 < 7.95
7.95 < 8.05
8.05 < 8.15
8.15 < 8.25
8.25 < 8.35
6
18
12
5
9
Rel
Frequency
0.12
0.36
0.24
0.10
0.18
Cum Rel Freq
0.12
0.48
0.72
0.82
1.00
Work each row to generate the missing frequency and/or relative frequency given a sample size
of 50. For example, first class: cum rel freq = rel freq = x/50 = 0.12, so x = 6. Complete the class
interval by recognizing that the second class beginning boundary is the end of the first interval's
boundary and using the class length calculated in the second class (0.10) to apply to all other
classes.
Difficulty: 3 Hard
Topic: Graphically Summarizing Quantitative Data
Learning Objective: 02-03 Summarize quantitative data using frequency distributions,
histograms, frequency polygons, and ogives.
Bloom's: Apply
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112
Copyright 2019 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior
written consent of McGraw-Hill Education.
111) Recently an advertising company called 200 people and asked them to identify the company
that was in an ad running nationwide. They obtained the following results.
Correctly recalled the company
Incorrectly recalled the company
Total
Female
66
44
110
Male
50
40
90
Total
116
84
200
Construct a table of row percentages.
Answer:
Correctly recalled the company
Incorrectly recalled the company
Female
56.9%
52.4%
Male
43.1%
47.6%
Total
100.0%
100.0%
Row percentages are calculated by dividing each part of the row by the total of the row and
multiplying by 100. For example, Female and correctly recalled = 66, which yields a row
percentage of (66/116)*100 = 56.9%.
Difficulty: 2 Medium
Topic: Contingency Tables
Learning Objective: 02-06 Examine the relationships between variables by using contingency
tables.
Bloom's: Apply
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113
Copyright 2019 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior
written consent of McGraw-Hill Education.
112) Recently an advertising company called 200 people and asked them to identify the company
that was in an ad running nationwide. They obtained the following results.
Correctly recalled the company
Incorrectly recalled the company
Total
Female
66
44
110
Male
50
40
90
Total
116
84
200
Construct a table of column percentages.
Answer:
Correctly recalled the company
Incorrectly recalled the company
Total
Female
60.0%
40.0%
100.0%
Male
55.6%
44.4%
100.0%
Column percentages are calculated by dividing each part of the column by the total of the
column and multiplying by 100. For example, Female and correctly recalled = 66, which yields a
column percentage of (66/110)*100 = 60.0%.
Difficulty: 2 Medium
Topic: Contingency Tables
Learning Objective: 02-06 Examine the relationships between variables by using contingency
tables.
Bloom's: Apply
AACSB: Analytical Thinking
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114
Copyright 2019 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior
written consent of McGraw-Hill Education.
113) A local electronics retailer recently conducted a study on purchasers of large screen
televisions. The study recorded the type of television and the credit account balance of the
customer at the time of purchase. They obtained the following results.
Credit Balance
Under $200
$200−$800
Over $800
Total
LED
10
S
16
34
LCD
16
12
12
40
Plasma
40
24
16
80
Projection
5
15
30
50
Construct a table of row percentages.
Answer:
Credit
Balance
Under $200
$200−$800
Over $800
LED
(10/71)*100 =
14.1%
(8/59)*100 =
13.6%
(16/74)*100 =
21.6%
LCD
(16/71)*100 =
22.5%
(12/59)*100 =
20.3%
(12/74)*100 =
16.2%
Plasma
(40/71)*100 =
56.3%
(24/59)*100 =
40.7%
(16/74)*100 =
21.6%
Projection
(5/71)*100 =
7.0%
(15/59)*100 =
25.4%
(30/74)*100 =
40.5%
Total
100.0%
100.0%
100.0%
Row percentages are calculated by dividing each part of the row by the total of the row and
multiplying by 100. Need to calculate the totals for each row (under $200 = 71; $200-$800 = 59;
over $800 = 74). For example, credit balance under $200 and LCD TV = 16, which yields row
percentage (16/71)*100 = 22.5%.
Difficulty: 2 Medium
Topic: Contingency Tables
Learning Objective: 02-06 Examine the relationships between variables by using contingency
tables.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
115
Copyright 2019 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior
written consent of McGraw-Hill Education.
114) A local electronics retailer recently conducted a study on purchasers of large screen
televisions. The study recorded the type of television and the credit account balance of the
customer at the time of purchase. They obtained the following results.
Credit Balance
Under $200
$200−$800
Over $800
Total
LED
10
S
16
34
LCD
16
12
12
40
Plasma
40
24
16
80
Projection
5
15
30
50
Construct a table of column percentages.
Answer:
Credit Balance
Under $200
$200−$800
Over $800
Total
LED
29.4%
23.5%
47.1%
100.0%
LCD
40.0%
30.0%
30.0%
100.0%
Plasma
50.0%
30.0%
20.0%
100.0%
Projection
10.0%
30.0%
60.0%
100.0%
Column percentages calculated by dividing each part of the column by the total of the column
and multiplying by 100. For example, credit balance under $200 and LCD TV = 16 yields row
percentage (16/40)*100 =40.0%.
Difficulty: 2 Medium
Topic: Contingency Tables
Learning Objective: 02-06 Examine the relationships between variables by using contingency
tables.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
116
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written consent of McGraw-Hill Education.
115) Math test anxiety can be found throughout the general population. A study of 116 seniors at
a local high school was conducted. The following table was produced from the data. Complete
the missing parts.
Score Range
Very anxious 37-50
Anxious/tense 33-36
Some mild anxiety 27-32
Generally relaxed 20-26
Very relaxed 10-19
Frequency
8
Rel Frequency Cum Freq Dist
0.19
0.26
24
0.67
0.33
Answer:
Score Range
Very anxious 37-50
Anxious/tense 33-36
Some mild anxiety 27-32
Generally relaxed 20-26
Very relaxed 10-19
Frequency
22
8
24
24
38
Rel
Frequency
0.19
0.07
0.207
0.207
0.33
Cum
Freq Dist
0.19
0.26
0.467
0.674
1.00
Work each row to generate the missing frequency and/or relative frequency given a sample size
of 116. For example, first class cum freq = rel freq = x/116 = 0.19, so x = 22. Use the definition
of cumulative frequency, which is the sum of the class relative frequency and the previous class
cumulative frequency (for example, "generally relaxed" relative frequency = 24/116 = .207,
which with a cumulative frequency of .67 gives the previous class of "some mild anxiety" a
cumulative frequency of .47).
Difficulty: 3 Hard
Topic: Graphically Summarizing Qualitative Data; Graphically Summarizing Quantitative Data
Learning Objective: 02-03 Summarize quantitative data using frequency distributions,
histograms, frequency polygons, and ogives.; 02-01 Summarize qualitative data by using
frequency distributions, bar charts, and pie charts.
Bloom's: Apply
AACSB: Analytical Thinking
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116) The number of weekly sales calls by a sample of 25 pharmaceutical salespersons is below.
24, 56, 43, 35, 37, 27, 29, 44, 34, 28, 33, 28, 46, 31, 38, 41, 48, 38, 27, 29, 37, 33, 31, 40, 50
Construct a histogram.
Answer:
Construct a frequency table. You can use five to seven classes, depending on your choice and
calculation of length as a whole integer.
Classes Midpoint
25
30
35
40
45
50
55
Frequency
3
6
6
4
3
2
1
While the frequency table and histogram shown above are technically valid, it is unlikely that a
student would create them based on the instructions in the textbook. A more likely frequency
table a student might create would be:
Class
24 < 31
31 < 38
38 < 45
45 < 52
52 < 59
Frequency
7
8
6
3
1
118
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A histogram could easily be derived from this frequency table.
Difficulty: 2 Medium
Topic: Graphically Summarizing Quantitative Data
Learning Objective: 02-03 Summarize quantitative data using frequency distributions,
histograms, frequency polygons, and ogives.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
117) The number of weekly sales calls by a sample of 25 pharmaceutical salespersons is below.
24, 56, 43, 35, 37, 27, 29, 44, 34, 28, 33, 28, 46, 31, 38, 41, 48, 38, 27, 29, 37, 33, 31, 40, 50
Construct a stem-and-leaf plot.
Answer: One possible stem-and-leaf display as might be created by Minitab:
Stem-and-Leaf of Sales Calls
N= 25
Leaf Unit = 1.0
1
7
12
(5)
8
4
2
1
2
2
3
3
4
4
5
5
4
778899
11334
57788
0134
68
0
6
Without Minitab, students would be unlikely to create the leftmost column with frequency
information.
The stem should be split and consist of 20, 30, 40, and 50. Leaves are the single units for the
number of sales calls (e.g., 20 stem: leaves = 4, 7, 7, 8, 8, 9, 9).
Difficulty: 2 Medium
Topic: Stem-and-Leaf Displays
Learning Objective: 02-05 Construct and interpret stem-and-leaf displays.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
119
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written consent of McGraw-Hill Education.
118) The number of weekly sales calls by a sample of 25 pharmaceutical salespersons is below.
24, 56, 43, 35, 37, 27, 29, 44, 34, 28, 33, 28, 46, 31, 38, 41, 48, 38, 27, 29, 37, 33, 31, 40, 50
Construct a frequency polygon.
Answer:
The frequency polygon is the line connecting the height (frequency) of the midpoint of each
class. Construct a frequency table.
Classes Midpoint
25
30
35
40
45
50
55
Frequency
3
6
6
4
3
2
1
While the frequency table and frequency polygon shown above are technically valid, it is
unlikely that a student would create them based on the instructions in the textbook. A more likely
frequency table a student might create would be:
Class
24 < 31
31 < 38
38 < 45
45 < 52
52 < 59
Frequency
7
8
6
3
1
A frequency polygon could easily be derived from this frequency table.
120
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written consent of McGraw-Hill Education.
Difficulty: 2 Medium
Topic: Graphically Summarizing Quantitative Data
Learning Objective: 02-03 Summarize quantitative data using frequency distributions,
histograms, frequency polygons, and ogives.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
121
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written consent of McGraw-Hill Education.
119) The following table lists the types of customer complaint calls on satellite TV service
during the first two months after installation.
No signal detected
Can't receive local channels
Missing channels
Intermittent reception
Remote control problems
Other issues
20%
14%
21%
8%
25%
12%
Construct a Pareto chart.
Answer:
A Pareto chart is a specialization of the bar chart used for categorical variables. The largest
percentage value is charted at the far left, and each problem percentage is graphed in decreasing
order. When showing "other" issues, always place that bar to the right because it includes an
accumulation of various reasons.
Difficulty: 2 Medium
Topic: Graphically Summarizing Qualitative Data
Learning Objective: 02-02 Construct and interpret Pareto charts.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
122
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written consent of McGraw-Hill Education.
120) The following data consist of the number of sick days taken by the 100 employees at a
small manufacturing company for the past 18 months. Construct a dot plot of these data and
describe the distribution.
5, 1, 4, 8, 0, 6, 3, 5, 3, 4, 7, 15, 5, 8, 2, 1, 5, 4
Answer:
Data are skewed to the right with one outlier.
A dot plot is constructed as a number line with minimum to maximum values (0 to 15).
Individual values are shown along the line as points (dots). With an outlier at the maximum
value, the shape has a tail to the right.
Difficulty: 2 Medium
Topic: Dot Plots
Learning Objective: 02-04 Construct and interpret dot plots.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
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written consent of McGraw-Hill Education.
1) The median is the measure of central tendency that divides a population or sample into four
equal parts.
Answer: FALSE
Explanation: The median divides a population into two equal parts.
Difficulty: 1 Easy
Topic: Describing Central Tendency
Learning Objective: 03-01 Compute and interpret the mean, median, and mode.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
2) The population mean is the average of the population measurements.
Answer: TRUE
Explanation: This mean is calculated by adding all of the population measurements and dividing
the resulting sum by the number of population measurements.
Difficulty: 2 Medium
Topic: Describing Central Tendency
Learning Objective: 03-01 Compute and interpret the mean, median, and mode.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
3) The mode is the measurement in a sample or population that occurs most frequently.
Answer: TRUE
Explanation: This is the measurement that occurs at the highest frequency.
Difficulty: 2 Medium
Topic: Describing Central Tendency
Learning Objective: 03-01 Compute and interpret the mean, median, and mode.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
124
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written consent of McGraw-Hill Education.
4) The population mean is the point estimate of the sample mean.
Answer: FALSE
Explanation: The sample mean is the point estimate of the population mean.
Difficulty: 2 Medium
Topic: Describing Central Tendency
Learning Objective: 03-01 Compute and interpret the mean, median, and mode.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
5) The median is said to be resistant to extreme values.
Answer: TRUE
Explanation: This is because the median divides the population or sample into two roughly
equal parts.
Difficulty: 2 Medium
Topic: Describing Central Tendency
Learning Objective: 03-01 Compute and interpret the mean, median, and mode.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
6) The range of the measurement is the largest measurement plus the smallest measurement.
Answer: FALSE
Explanation: The range is the largest minus the smallest measurement.
Difficulty: 2 Medium
Topic: Measures of Variation
Learning Objective: 03-02 Compute and interpret the range, variance, and standard deviation.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
7) The population variance is the average of the squared deviations of the individual population
measurements from the population mean.
Answer: TRUE
Explanation: This population variance is represented by sigma squared.
Difficulty: 2 Medium
Topic: Measures of Variation
Learning Objective: 03-02 Compute and interpret the range, variance, and standard deviation.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
8) In a symmetric population, the median equals the mode.
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Answer: TRUE
Explanation: The population is a perfect bell curve.
Difficulty: 2 Medium
Topic: Describing Central Tendency
Learning Objective: 03-01 Compute and interpret the mean, median, and mode.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
9) It is appropriate to use the Empirical Rule to describe a population that is extremely skewed.
Answer: FALSE
Explanation: The Empirical Rule should be used for normally distributed populations.
Difficulty: 2 Medium
Topic: Measures of Variation
Learning Objective: 03-03 Use the Empirical Rule and Chebyshev's Theorem to describe
variation.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
10) The median is the value below which and above which approximately 50 percent of the
measurements lie.
Answer: TRUE
Explanation: It is the central tendency of a population and evenly splits the population or sample
into two.
Difficulty: 1 Easy
Topic: Describing Central Tendency
Learning Objective: 03-01 Compute and interpret the mean, median, and mode.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
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written consent of McGraw-Hill Education.
11) If there are seven classes in a frequency distribution, then the fourth class will always contain
the median.
Answer: FALSE
Explanation: The median is the middle measurement of the data set. Depending on the shape of
the distribution, the median can be in any of the classes.
Difficulty: 2 Medium
Topic: Describing Central Tendency
Learning Objective: 03-01 Compute and interpret the mean, median, and mode.
Bloom's: Evaluate
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
12) Range is a better measure of variation than standard deviation.
Answer: FALSE
Explanation: The standard deviation is a better measure of variability than range.
Difficulty: 2 Medium
Topic: Measures of Variation
Learning Objective: 03-02 Compute and interpret the range, variance, and standard deviation.
Bloom's: Understand
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
13) The mean is one component of the five-number summary.
Answer: FALSE
Explanation: The five-number summary includes Q1, Q2, Q3, and the smallest and largest
measurements.
Difficulty: 2 Medium
Topic: Percentiles, Quartiles, and Box-and-Whisker Displays
Learning Objective: 03-04 Compute and interpret percentiles, quartiles, and box-and-whiskers
displays.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
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written consent of McGraw-Hill Education.
14) The pth percentile is a value such that (100 − p) percent of the measurements fall at or below
the value.
Answer: FALSE
Explanation: The pth percentile is a value such that p percent of the measurements fall at or
below the value.
Difficulty: 2 Medium
Topic: Percentiles, Quartiles, and Box-and-Whisker Displays
Learning Objective: 03-04 Compute and interpret percentiles, quartiles, and box-and-whiskers
displays.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
15) Chebyshev's Theorem is only of practical use when analyzing a non-mound-shaped
population that is not very skewed.
Answer: TRUE
Explanation: This theorem gives large intervals containing reasonably large fractions of the
population units no matter what the population's shape might be.
Difficulty: 2 Medium
Topic: Measures of Variation
Learning Objective: 03-03 Use the Empirical Rule and Chebyshev's Theorem to describe
variation.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
16) Z-score is often used as a measure of risk.
Answer: FALSE
Explanation: Z-score is used to measure a measurement's distance from the mean.
Difficulty: 2 Medium
Topic: Measures of Variation
Learning Objective: 03-03 Use the Empirical Rule and Chebyshev's Theorem to describe
variation.
Bloom's: Understand
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
128
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written consent of McGraw-Hill Education.
17) A correlation coefficient close to −1 says x and y are highly related.
Answer: TRUE
Explanation: This means they have a strong tendency to move together in a straight-line fashion.
Difficulty: 1 Easy
Topic: Covariance, Correlation, and the Least Squares Line
Learning Objective: 03-05 Compute and interpret covariance, correlation, and the least squares
line.
Bloom's: Understand
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
18) The line that minimizes the sum of the squared horizontal (x) distances between the points on
the scatter plot and the line is the least squares line.
Answer: FALSE
Explanation: The definition of the least squares line is the line that minimizes the sum of the
squared vertical distances (y) between the points.
Difficulty: 3 Hard
Topic: Covariance, Correlation, and the Least Squares Line
Learning Objective: 03-05 Compute and interpret covariance, correlation, and the least squares
line.
Bloom's: Understand
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
19) The weights that are used in calculating a weighted mean will vary depending on the
situation.
Answer: TRUE
Explanation: The idea is to choose weights that represent the relative importance of the
measurements in the population or sample.
Difficulty: 2 Medium
Topic: Weighted Means and Grouped Data
Learning Objective: 03-06 Compute and interpret weighted means and the mean standard
deviation of grouped data.
Bloom's: Understand
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
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written consent of McGraw-Hill Education.
20) Data summarized in a frequency distribution or histogram form are often called weighted
data.
Answer: FALSE
Explanation: Data summarized in a frequency distribution or histogram form are called grouped
data.
Difficulty: 2 Medium
Topic: Weighted Means and Grouped Data
Learning Objective: 03-06 Compute and interpret weighted means and the mean standard
deviation of grouped data.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
21) In the calculation of a mean for grouped data, we assume that the average of the
measurements in each class equals the class midpoint.
Answer: TRUE
Explanation: We do this because we cannot compute and exact value for the mean.
Difficulty: 2 Medium
Topic: Weighted Means and Grouped Data
Learning Objective: 03-06 Compute and interpret weighted means and the mean standard
deviation of grouped data.
Bloom's: Understand
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
22) The geometric mean is the rate of change that yields better wealth at the end of a set of time
periods than the actual returns.
Answer: FALSE
Explanation: The definition of geometric mean is the rate of change that yields the same wealth
at the end of several time periods as do actual returns.
Difficulty: 3 Hard
Topic: Geometric Mean
Learning Objective: 03-07 Compute and interpret the geometric mean.
Bloom's: Understand
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
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written consent of McGraw-Hill Education.
23) When calculating the geometric mean, a quantity of 1 is added to the nth root of the product
(1 + R1)(1 + R2) . . . (1 + Rn).
Answer: FALSE
Explanation: When calculating the geometric mean, 1 is subtracted from the nth root of the
product.
Difficulty: 3 Hard
Topic: Geometric Mean
Learning Objective: 03-07 Compute and interpret the geometric mean.
Bloom's: Understand
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
24) The ending value of an initial investment can be calculated using weighted means.
Answer: FALSE
Explanation: The ending value of an initial investment is calculated using geometric mean.
Difficulty: 2 Medium
Topic: Geometric Mean
Learning Objective: 03-07 Compute and interpret the geometric mean.
Bloom's: Understand
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
25) A normal population has 99.73 percent of the population measurements within ________
standard deviation(s) of the mean.
A) 1
B) 2
C) 3
D) 4
Answer: C
Explanation: This is part of the Empirical Rule for a normally distributed population.
Difficulty: 2 Medium
Topic: Measures of Variation
Learning Objective: 03-03 Use the Empirical Rule and Chebyshev's Theorem to describe
variation.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
131
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written consent of McGraw-Hill Education.
26) All of the following are measures of central tendency except the ________.
A) range
B) mode
C) mean
D) median
Answer: A
Explanation: The range gives the lowest to the highest value in the sample or population.
Difficulty: 1 Easy
Topic: Describing Central Tendency
Learning Objective: 03-01 Compute and interpret the mean, median, and mode.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
27) Which percentile describes the first quartile, Q1?
A) 25th
B) 50th
C) 75th
D) 100th
Answer: A
Explanation: This is denoted at Q1, a value below which approximately 25 percent of the
measurements lie.
Difficulty: 1 Easy
Topic: Percentiles, Quartiles, and Box-and-Whisker Displays
Learning Objective: 03-04 Compute and interpret percentiles, quartiles, and box-and-whiskers
displays.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
132
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written consent of McGraw-Hill Education.
28) Which percentile describes the third quartile, Q3?
A) 25th
B) 50th
C) 75th
D) 100th
Answer: C
Explanation: This is denoted as Q3, a value below which approximately 75 percent of the
measurements lie.
Difficulty: 1 Easy
Topic: Percentiles, Quartiles, and Box-and-Whisker Displays
Learning Objective: 03-04 Compute and interpret percentiles, quartiles, and box-and-whiskers
displays.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
29) Which of the following is influenced the least by the occurrence of extreme values in a
sample?
A) mean
B) median
C) geometric mean
D) weighted mean
Answer: B
Explanation: The median looks at the middle of a sample or population and does not take into
effect low or high values.
Difficulty: 2 Medium
Topic: Describing Central Tendency
Learning Objective: 03-01 Compute and interpret the mean, median, and mode.
Bloom's: Understand
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
133
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written consent of McGraw-Hill Education.
30) If a population distribution is skewed to the right, then, given a random sample from that
population, one would expect that the ________.
A) median would be greater than the mean
B) mode would be equal to the mean
C) median would be less than the mean
D) median would be equal to the mean
Answer: C
Explanation: The median in this case would be a better representation of the population —
showing where most of the numbers congregate.
Difficulty: 3 Hard
Topic: Describing Central Tendency
Learning Objective: 03-01 Compute and interpret the mean, median, and mode.
Bloom's: Evaluate
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
31) If the mean, median, and mode for a given population are all equal and the relative frequency
curve has matching tails to the right and left, then we would describe the shape of the distribution
of the population as ________.
A) bimodal
B) skewed to the right
C) symmetrical
D) skewed to the left
Answer: C
Explanation: A symmetrical bell curve.
Difficulty: 3 Hard
Topic: Describing Central Tendency
Learning Objective: 03-01 Compute and interpret the mean, median, and mode.
Bloom's: Understand
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
134
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written consent of McGraw-Hill Education.
32) A disadvantage of using grouping (a frequency table) with sample data is that
A) calculations involving central tendency and variation are more complicated than central
tendency and variation calculations based on ungrouped data.
B) the descriptive statistics are less precise than the descriptive statistics obtained using
ungrouped data.
C) the interpretation of the grouped data descriptive statistics is meaningless.
D) it is much more difficult to summarize the information than it is with the ungrouped data.
Answer: B
Explanation: This is because we do not have access to the individual values; only the grouped
data values.
Difficulty: 3 Hard
Topic: Weighted Means and Grouped Data
Learning Objective: 03-06 Compute and interpret weighted means and the mean standard
deviation of grouped data.
Bloom's: Evaluate
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
33) When using Chebyshev's Theorem to obtain the bounds for 99.73 percent of the values in a
population, the interval generally will be ________ the interval obtained for the same percentage
if a normal distribution is assumed (Empirical Rule).
A) shorter than
B) wider than
C) the same as
Answer: B
Explanation: This is due to the fact that Chebyshev's Theorem is used for non-mound shaped
populations.
Difficulty: 3 Hard
Topic: Measures of Variation
Learning Objective: 03-03 Use the Empirical Rule and Chebyshev's Theorem to describe
variation.
Bloom's: Apply
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
135
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written consent of McGraw-Hill Education.
34) A quantity that measures the variation of a population or a sample relative to its mean is
called the ________.
A) range
B) standard deviation
C) coefficient of variation
D) variance
E) interquartile range
Answer: C
Explanation: The formula is the standard deviation divided by the mean then multiplied by 100.
Difficulty: 1 Easy
Topic: Measures of Variation
Learning Objective: 03-02 Compute and interpret the range, variance, and standard deviation.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
35) As a measure of variation, the sample ________ is easy to understand and compute. It is
based on the two extreme values and therefore may reflect an extreme measurement that is not
entirely representative of the data set's variation.
A) range
B) standard deviation
C) variance
D) interquartile range
E) coefficient of variation
Answer: A
Explanation: The range simply gives the highest and lowest numbers and does not give any
central tendencies about the data.
Difficulty: 2 Medium
Topic: Measures of Variation
Learning Objective: 03-02 Compute and interpret the range, variance, and standard deviation.
Bloom's: Understand
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
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written consent of McGraw-Hill Education.
36) A measurement located outside the upper limits of a box-and-whiskers display is ________.
A) always in the first quartile
B) an outlier
C) always the largest value in the data set
D) within the lower limits
Answer: B
Explanation: The box gives you the range from the first to the third quartile.
Difficulty: 2 Medium
Topic: Percentiles, Quartiles, and Box-and-Whisker Displays
Learning Objective: 03-04 Compute and interpret percentiles, quartiles, and box-and-whiskers
displays.
Bloom's: Understand
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
37) Another name for the 50th percentile is the ________.
A) mean
B) first quartile
C) median
D) mode
E) third quartile
Answer: C
Explanation: The median is the middle number of a sample or population.
Difficulty: 2 Medium
Topic: Percentiles, Quartiles, and Box-and-Whisker Displays
Learning Objective: 03-04 Compute and interpret percentiles, quartiles, and box-and-whiskers
displays.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
137
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written consent of McGraw-Hill Education.
38) The measurement in a sample or a population that occurs most frequently is the ________.
A) mode
B) mean
C) median
D) outlier
E) average
Answer: A
Explanation: There can be two modes.
Difficulty: 2 Medium
Topic: Describing Central Tendency
Learning Objective: 03-01 Compute and interpret the mean, median, and mode.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
39) The average of the squared deviations of the individual population measurement from the
population mean is the ________.
A) standard deviation
B) mean
C) variance
D) median
E) range
Answer: C
Explanation: This number is represented by sigma and is calculated via the standard deviation.
Difficulty: 2 Medium
Topic: Measures of Variation
Learning Objective: 03-02 Compute and interpret the range, variance, and standard deviation.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
138
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written consent of McGraw-Hill Education.
40) If the mean is greater than the median, then the relative frequency curve is most likely to be
________.
A) skewed right
B) skewed left
C) symmetrical
D) bimodal
Answer: A
Explanation: The median is not affected by outliers.
Difficulty: 2 Medium
Topic: Describing Central Tendency
Learning Objective: 03-01 Compute and interpret the mean, median, and mode.
Bloom's: Understand
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
41) The ________ is the positive square root of the sample variance.
A) sample mean
B) sample standard deviation
C) range
D) median
E) population standard deviation
Answer: B
Explanation: It is represented by sigma and shows how far values are from the mean.
Difficulty: 2 Medium
Topic: Measures of Variation
Learning Objective: 03-02 Compute and interpret the range, variance, and standard deviation.
Bloom's: Understand
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
139
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written consent of McGraw-Hill Education.
42) The ________ is a quantity that measures the variation of a population or sample relative to
its mean.
A) mean
B) standard deviation
C) range
D) coefficient of variation
E) Z-score
Answer: D
Explanation: It is found by dividing the standard deviation by the mean and multiplying by 100.
Difficulty: 2 Medium
Topic: Measures of Variation
Learning Objective: 03-02 Compute and interpret the range, variance, and standard deviation.
Bloom's: Understand
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
43) An interval that contains a specified percentage of the individual measurements is called a(n)
________ interval.
A) three-sigma
B) tolerance
C) normal
D) empirical
Answer: B
Explanation: It can be used with the normally distributed population.
Difficulty: 2 Medium
Topic: Measures of Variation
Learning Objective: 03-03 Use the Empirical Rule and Chebyshev's Theorem to describe
variation.
Bloom's: Understand
AACSB: Reflective Thinking
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140
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44) As the coefficient of variation ________, risk ________.
A) increases; decreases
B) decreases; increases
C) increases; increases
D) remains constant; increases
Answer: C
Explanation: The coefficient of variation can be used as a measure of risk because it can
measure the rate on return.
Difficulty: 2 Medium
Topic: Measures of Variation
Learning Objective: 03-03 Use the Empirical Rule and Chebyshev's Theorem to describe
variation.
Bloom's: Evaluate
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
45) Which of the following is a measure of the strength of the linear relationship between x and y
that is dependent on the units in which x and y are measured?
A) covariance
B) correlation coefficient
C) slope
D) least squares line
Answer: A
Explanation: This tells you how close the relationship is to a straight line between x and y.
Difficulty: 2 Medium
Topic: Covariance, Correlation, and the Least Squares Line
Learning Objective: 03-05 Compute and interpret covariance, correlation, and the least squares
line.
Bloom's: Understand
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
141
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written consent of McGraw-Hill Education.
46) If b0 = 32 and b1 = −4 and the predicted value of y is 14, what is the value of x?
A) −24.0
B) 18.0
C) 4.5
D) .56
Answer: C
Explanation: y − b1x = b0
14 − (−4)x = 32
4x = 18
x = 4.5
Difficulty: 3 Hard
Topic: Covariance, Correlation, and the Least Squares Line
Learning Objective: 03-05 Compute and interpret covariance, correlation, and the least squares
line.
Bloom's: Apply
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
47) In the least squares line, ________ is defined as rise/run.
A) correlation coefficient
B) predicted value of y
C) y-intercept
D) slope
Answer: D
Explanation: The slope can be positive or negative, and that determines the correlation.
Difficulty: 1 Easy
Topic: Covariance, Correlation, and the Least Squares Line
Learning Objective: 03-05 Compute and interpret covariance, correlation, and the least squares
line.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
142
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written consent of McGraw-Hill Education.
48) In the calculation of a mean for grouped data, ________ are used.
A) total sample size and sum of the midpoints of each class
B) total sample size and sum of the weighted midpoints
C) sum of the frequency of each class and the sum of the midpoints of each class
D) sum of the frequency of each class and the sample midpoint
Answer: B
Explanation: Total sample size and sum of the weighted midpoint are used, so therefore we
cannot make many predictions about the individual data.
Difficulty: 3 Hard
Topic: Weighted Means and Grouped Data
Learning Objective: 03-06 Compute and interpret weighted means and the mean standard
deviation of grouped data.
Bloom's: Understand
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
49) The arithmetic mean is ________ larger than a weighted mean in a set of data that uses
unequal weights.
A) always
B) sometimes
C) never
Answer: B
Explanation: The arithmetic mean is useful, but it is not a good measure of the rate of change
exhibited by a variable over time.
Difficulty: 3 Hard
Topic: Weighted Means and Grouped Data
Learning Objective: 03-06 Compute and interpret weighted means and the mean standard
deviation of grouped data.
Bloom's: Understand
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
143
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written consent of McGraw-Hill Education.
50) The constant return that yields the same wealth at the end of the investment period as do the
actual returns is the ________.
A) grouped mean
B) geometric mean
C) weighted mean
D) arithmetic mean
Answer: B
Explanation: This helps to remedy the issue with the arithmetic mean since it is not useful to
display change over time.
Difficulty: 1 Easy
Topic: Geometric Mean
Learning Objective: 03-07 Compute and interpret the geometric mean.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
51) In a statistics class, the following 10 scores were randomly selected: 74, 73, 77, 77, 71, 68,
65, 77, 67, 66.
What is the mean?
A) 71.5
B) 72.0
C) 77.0
D) 71.0
E) 73.0
Answer: A
Explanation: 74 + 73 + 77 + 77 +71 + 68 + 65 + 77 + 67 + 66 ÷ 10 = 71.5
Difficulty: 1 Easy
Topic: Describing Central Tendency
Learning Objective: 03-01 Compute and interpret the mean, median, and mode.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
144
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written consent of McGraw-Hill Education.
52) In a statistics class, the following 10 scores were randomly selected: 74, 73, 77, 77, 71, 68,
65, 77, 67, 66.
What is the median?
A) 71.5
B) 72.0
C) 77.0
D) 71.0
E) 73.0
Answer: B
Explanation: 65, 66, 67, 68, 71, 73, 74, 77, 77, 77
(71 + 73) ÷ 2 = 72
Difficulty: 1 Easy
Topic: Describing Central Tendency
Learning Objective: 03-01 Compute and interpret the mean, median, and mode.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
53) In a statistics class, the following 10 scores were randomly selected: 74, 73, 77, 77, 71, 68,
65, 77, 67, 66.
What is the mode?
A) 71.5
B) 72.0
C) 77.0
D) 71.0
E) 73.0
Answer: C
Explanation: 77 appears the most frequently in this data set.
Difficulty: 1 Easy
Topic: Describing Central Tendency
Learning Objective: 03-01 Compute and interpret the mean, median, and mode.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
145
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written consent of McGraw-Hill Education.
54) In a hearing test, subjects estimate the loudness (in decibels) of a sound, and the results are:
68, 67, 70, 71, 68, 75, 68, 62, 80, 73, 68.
What is the mean?
A) 70
B) 75
C) 68
D) 71
E) 80
Answer: A
Explanation: 68 + 67 + 70 + 71 + 68 + 75 + 68 + 62 + 80 + 73 + 68 ÷ 11 = 70
Difficulty: 1 Easy
Topic: Describing Central Tendency
Learning Objective: 03-01 Compute and interpret the mean, median, and mode.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
55) In a hearing test, subjects estimate the loudness (in decibels) of a sound, and the results are:
68, 67, 70, 71, 68, 75, 68, 62, 80, 73, 68.
What is the median?
A) 70
B) 75
C) 68
D) 71
E) 80
Answer: C
Explanation: 62, 67, 68, 68, 68, 68, 70, 71, 73, 75, 80
68 is the middle number.
Difficulty: 1 Easy
Topic: Describing Central Tendency
Learning Objective: 03-01 Compute and interpret the mean, median, and mode.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
146
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written consent of McGraw-Hill Education.
56) In a hearing test, subjects estimate the loudness (in decibels) of a sound, and the results are:
68, 67, 70, 71, 68, 75, 68, 62, 80, 73, 68.
What is the mode?
A) 70
B) 75
C) 68
D) 71
E) 80
Answer: C
Explanation: 68 appears most frequently in this data set.
Difficulty: 1 Easy
Topic: Describing Central Tendency
Learning Objective: 03-01 Compute and interpret the mean, median, and mode.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
57) The local amusement park was interested in the average wait time at their most popular roller
coaster at the peak park time (2 p.m.). They selected 13 patrons and had them get in line between
2 and 3 p.m. Each was given a stopwatch to record the time they spent in line. The times
recorded were as follows (in minutes): 118, 124, 108, 116, 99, 120, 148, 118, 119, 121, 45, 130,
118.
What is the mean?
A) 114.15
B) 118
C) 148
D) 45
E) 115.5
Answer: A
Explanation: Mean = sum of values/n = 1484/13 = 114.15
Difficulty: 1 Easy
Topic: Describing Central Tendency
Learning Objective: 03-01 Compute and interpret the mean, median, and mode.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
147
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written consent of McGraw-Hill Education.
58) The local amusement park was interested in the average wait time at their most popular roller
coaster at the peak park time (2 p.m.). They selected 13 patrons and had them get in line between
2 and 3 p.m. Each was given a stopwatch to record the time they spent in line. The times
recorded were as follows (in minutes): 118, 124, 108, 116, 99, 120, 148, 118, 119, 121, 45, 130,
118.
What is the median?
A) 114.15
B) 118
C) 148
D) 45
E) 115.5
Answer: B
Explanation: To calculate median, put data measurements in ascending order. The median for an
odd number of measurements is the middle measurement; median = 118.
Difficulty: 1 Easy
Topic: Describing Central Tendency
Learning Objective: 03-01 Compute and interpret the mean, median, and mode.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
59) The local amusement park was interested in the average wait time at their most popular roller
coaster at the peak park time (2 p.m.). They selected 13 patrons and had them get in line between
2 and 3 p.m. Each was given a stopwatch to record the time they spent in line. The times
recorded were as follows (in minutes): 118, 124, 108, 116, 99, 120, 148, 118, 119, 121, 45, 130,
118.
What is the mode?
A) 114.15
B) 118
C) 148
D) 45
E) 115.5
Answer: B
Explanation: Mode is the value(s) that appears most frequently; mode = 118 (occurs three
times).
Difficulty: 1 Easy
Topic: Describing Central Tendency
Learning Objective: 03-01 Compute and interpret the mean, median, and mode.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
148
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written consent of McGraw-Hill Education.
60) Quality control is an important issue at ACME Company, which manufactures light bulbs.
To test the life-hours of their light bulbs, they randomly sampled nine light bulbs and measured
how many hours they lasted: 378, 361, 350, 375, 200, 391, 375, 368, 321.
What is the mean?
A) 375
B) 368
C) 389.9
D) 200
E) 346.6
Answer: E
Explanation: Mean = sum of values/n = 3119/9 = 346.56, or 346.6.
Difficulty: 1 Easy
Topic: Describing Central Tendency
Learning Objective: 03-01 Compute and interpret the mean, median, and mode.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
61) Quality control is an important issue at ACME Company, which manufactures light bulbs.
To test the life-hours of their light bulbs, they randomly sampled nine light bulbs and measured
how many hours they lasted: 378, 361, 350, 375, 200, 391, 375, 368, 321.
What is the median?
A) 375
B) 368
C) 389.9
D) 200
E) 346.6
Answer: B
Explanation: To calculate median, put data measurements in ascending order. The median for an
odd number of measurements is the middle measurement; median = 368.
Difficulty: 1 Easy
Topic: Describing Central Tendency
Learning Objective: 03-01 Compute and interpret the mean, median, and mode.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
149
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written consent of McGraw-Hill Education.
62) Quality control is an important issue at ACME Company, which manufactures light bulbs.
To test the life-hours of their light bulbs, they randomly sampled nine light bulbs and measured
how many hours they lasted: 378, 361, 350, 375, 200, 391, 375, 368, 321.
What is the mode?
A) 375
B) 368
C) 389.9
D) 200
E) 346.6
Answer: A
Explanation: Mode is the value(s) that appears most frequently; mode = 375 (occurs two times).
Difficulty: 1 Easy
Topic: Describing Central Tendency
Learning Objective: 03-01 Compute and interpret the mean, median, and mode.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
63) Find the coefficient of variation for IQ tests with a mean of 100 and a standard deviation of
15.
A) 15.0
B) 6.7
C) .15
D) 1.5
E) 67
Answer: A
Explanation: Coefficient of variation = (Std dev/mean) × 100 = (15/100) × 100 = 15
Difficulty: 3 Hard
Topic: Measures of Variation
Learning Objective: 03-02 Compute and interpret the range, variance, and standard deviation.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
150
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written consent of McGraw-Hill Education.
64) Find the z-score for an IQ test score of 142 when the mean is 100 and the standard deviation
is 15.
A) 42
B) 2.8
C) 18.78
D) 1.27
E) −2.8
Answer: B
Explanation: Z-score = (x − mean)/std dev = (142 − 100)/15 = 42/15 = 2.8
Difficulty: 2 Medium
Topic: Measures of Variation
Learning Objective: 03-02 Compute and interpret the range, variance, and standard deviation.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
65) Find the z-score for an IQ test score of 92 when the mean is 100 and the standard deviation is
15.
A) .53
B) .77
C) −.77
D) −.53
E) −8.00
Answer: D
Explanation: Z-score = (x − mean)/std dev = (92 − 100)/15 = −8/15 = −.53
Difficulty: 2 Medium
Topic: Measures of Variation
Learning Objective: 03-02 Compute and interpret the range, variance, and standard deviation.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
151
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written consent of McGraw-Hill Education.
66) Find the z-score for an IQ test score of 118 when the mean is 100 and the standard deviation
is 15.
A) 1.2
B) 1.0
C) 18.0
D) −1.03
E) −1.2
Answer: A
Explanation: Z-score = (x − mean)/std dev = (118 − 100)/15 = 18/15 = 1.2
Difficulty: 2 Medium
Topic: Measures of Variation
Learning Objective: 03-02 Compute and interpret the range, variance, and standard deviation.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
67) Find the z-score for an IQ test score of 125 when the mean is 100 and the standard deviation
is 15.
A) 25
B) 1.1
C) 1.67
D) −1.1
E) −1.67
Answer: C
Explanation: Z-score = (x − mean)/std dev = (125 − 100)/15 = 25/15 = 1.67
Difficulty: 2 Medium
Topic: Measures of Variation
Learning Objective: 03-02 Compute and interpret the range, variance, and standard deviation.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
152
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written consent of McGraw-Hill Education.
68) Using Chebyshev's Theorem, find the interval that contains at least 93.75 percent of all
measurements when the mean = 2.549 and s = 1.828.
A) [−2.935, 8.033]
B) [−1.107, 6.205]
C) [−26.699, 31.797]
D) [2.435, 2.663]
E) [−4.763, 9.861]
Answer: E
Explanation: 1 − (1/k2) = .9375; 1/k2 = 1 − .9375; 1/k =
;k=4
Difficulty: 3 Hard
Topic: Measures of Variation
Learning Objective: 03-03 Use the Empirical Rule and Chebyshev's Theorem to describe
variation.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
69) According to a survey of the top 10 employers in a major city in the Midwest, a worker
spends an average of 413 minutes a day on the job. Suppose the standard deviation is 26.8
minutes, and the time spent is approximately a normal distribution.
What are the times within which approximately 68.26 percent of all workers will fall?
A) [394.8, 431.2]
B) [386.2, 439.8]
C) [372.8, 453.2]
D) [359.4, 466.6]
E) [332.6, 493.4]
Answer: B
Explanation: 413 − 26.8 = 386.2
413 + 26.8 = 439.8
Difficulty: 2 Medium
Topic: Measures of Variation
Learning Objective: 03-03 Use the Empirical Rule and Chebyshev's Theorem to describe
variation.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
153
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written consent of McGraw-Hill Education.
70) According to a survey of the top 10 employers in a major city in the Midwest, a worker
spends an average of 413 minutes a day on the job. Suppose the standard deviation is 26.8
minutes and the time spent is approximately a normal distribution.
What are the times within which approximately 99.73 percent of all workers will fall?
A) [305.8, 520.2]
B) [386.2, 439.8]
C) [372.8, 453.2]
D) [359.4, 466.6]
E) [332.6, 493.4]
Answer: E
Explanation: 3(26.8) − 413 = 332.6
3(26.8) + 413 = 493.4
Difficulty: 2 Medium
Topic: Measures of Variation
Learning Objective: 03-03 Use the Empirical Rule and Chebyshev's Theorem to describe
variation.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
71) According to Chebyshev's theorem, at least what proportion of the data will be within μ ± kσ
for k = 2?
A) 68%
B) 50%
C) 25%
D) 75%
E) 34%
Answer: D
Explanation: For any values of k greater than 1, at least 100(1 − 1 /k2)% of the population
measurements lie in the interval.
Difficulty: 2 Medium
Topic: Measures of Variation
Learning Objective: 03-03 Use the Empirical Rule and Chebyshev's Theorem to describe
variation.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
154
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written consent of McGraw-Hill Education.
72) Using Chebyshev's theorem, approximate the minimum proportion of the data that will be
within μ ± kσ for k = 1.6.
A) 39%
B) 58%
C) 68%
D) 61%
E) 92%
Answer: D
Explanation: 100(1 − 1 /k2)% = 100(1 − 1 /1.62)% = 61%
Difficulty: 2 Medium
Topic: Measures of Variation
Learning Objective: 03-03 Use the Empirical Rule and Chebyshev's Theorem to describe
variation.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
73) Using Chebyshev's theorem, approximate the minimum proportion of the data that will be
within μ ± kσ for k = 3.2.
A) 90%
B) 95%
C) 84%
D) 97%
E) 10%
Answer: A
Explanation: 100(1 − 1 /k2)% = 100(1 − 1 /3.22)% = 90%
Difficulty: 2 Medium
Topic: Measures of Variation
Learning Objective: 03-03 Use the Empirical Rule and Chebyshev's Theorem to describe
variation.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
155
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written consent of McGraw-Hill Education.
74) According to Chebyshev's theorem, a range of how many standard deviations would include
at least 80 percent of the values?
A) 5.0
B) 2.2
C) 2.5
D) 1.6
E) 2.0
Answer: B
Explanation: 100(1 − 1 /k2)% = 100(1 − 1 /2.22)% = 80%
Difficulty: 3 Hard
Topic: Measures of Variation
Learning Objective: 03-03 Use the Empirical Rule and Chebyshev's Theorem to describe
variation.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
75) In a statistics class, 10 scores were randomly selected with the following results (mean =
71.5): 74, 73, 77, 77, 71, 68, 65, 77, 67, 66.
What is the range?
A) 22.72
B) 12.00
C) 4.77
D) 516.20
E) 144.00
Answer: B
Explanation:
65, 66, 67, 68, 71, 73, 74, 77, 77, 77
77 − 65 = 12
Difficulty: 1 Easy
Topic: Measures of Variation
Learning Objective: 03-02 Compute and interpret the range, variance, and standard deviation.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
156
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written consent of McGraw-Hill Education.
76) In a statistics class, 10 scores were randomly selected with the following results (mean =
71.5): 74, 73, 77, 77, 71, 68, 65, 77, 67, 66.
What is the variance?
A) 22.72
B) 12.00
C) 4.77
D) 516.20
E) 144.00
Answer: A
Explanation: (74 − 71.5) = 2.5 squared = 6.25
(73 − 71.5) = 1.5 squared = 2.25
(77 − 71.5) = 5.5 squared = 30.25
(77 − 71.5) = 5.5 squared = 30.25
(71 − 71.5) = 0.5 squared = 0.25
(68 − 71.5) = −3.5 squared = 12.25
(65 − 71.5) = −6.5 squared = 42.25
(77 − 71.5) = 5.5 squared = 30.25
(67 − 71.5) = −4.5 squared = 20.25
(66 − 71.5) = −5.5 squared = 30.25
(6.25 + 2.25 + 30.25 + 30.25 + 0.25 + 12.25 +42.25 + 30.25 + 20.25 + 30.25) = 204.5 / 9 = 22.72
Difficulty: 2 Medium
Topic: Measures of Variation
Learning Objective: 03-02 Compute and interpret the range, variance, and standard deviation.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
77) In a statistics class, 10 scores were randomly selected with the following results (mean =
71.5): 74, 73, 77, 77, 71, 68, 65, 77, 67, 66.
What is the standard deviation?
A) 22.72
B) 12.00
C) 4.77
D) 516.20
E) 144.00
Answer: C
Explanation: You take the square root of 22.71 = 4.77
Difficulty: 2 Medium
Topic: Measures of Variation
Learning Objective: 03-02 Compute and interpret the range, variance, and standard deviation.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
157
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written consent of McGraw-Hill Education.
78) In a hearing test, randomly selected subjects estimate the loudness (in decibels) of a sound,
and the results are (mean = 70): 68, 67, 70, 71, 68, 75, 68, 62, 80, 73, 68.
What is the range?
A) 18
B) 4.73
C) 22.40
D) 324
E) 6.76
Answer: A
Explanation: 62, 67, 68, 68, 68, 68, 70, 71, 73, 75, 80
80 − 62 = 18
Difficulty: 1 Easy
Topic: Measures of Variation
Learning Objective: 03-02 Compute and interpret the range, variance, and standard deviation.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
158
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written consent of McGraw-Hill Education.
79) In a hearing test, randomly selected subjects estimate the loudness (in decibels) of a sound,
and the results are (mean = 70): 68, 67, 70, 71, 68, 75, 68, 62, 80, 73, 68.
What is the variance?
A) 18
B) 4.73
C) 22.40
D) 324
E) 6.76
Answer: C
Explanation: 62, 67, 68, 68, 68, 68, 70, 71, 73, 75, 80
(62 − 70)= -8 squared = 64
(67 − 70)= -3 squared = 9
(68 − 70)= -2 squared = 4
(68 − 70)= -2 squared = 4
(68 − 70)= -2 squared = 4
(68 − 70)= -2 squared = 4
(70 − 70)= 0 squared = 0
(71 − 70)= 1 squared = 1
(73 − 70)= 2 squared = 4
(75 − 70)= 5 squared = 25
(80 − 70)= 10 squared = 100
(64 + 9 + 4 + 4 + 4 + 4 + 0 + 1 + 4 + 25 + 100) = 224 / 10 = 22.40
Difficulty: 2 Medium
Topic: Measures of Variation
Learning Objective: 03-02 Compute and interpret the range, variance, and standard deviation.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
159
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written consent of McGraw-Hill Education.
80) In a hearing test, randomly selected subjects estimate the loudness (in decibels) of a sound,
and the results are (mean = 70): 68, 67, 70, 71, 68, 75, 68, 62, 80, 73, 68.
What is the standard deviation?
A) 18
B) 4.73
C) 22.40
D) 324
E) 6.76
Answer: B
Explanation: You take the square root of 22.40 = 4.73
Difficulty: 2 Medium
Topic: Measures of Variation
Learning Objective: 03-02 Compute and interpret the range, variance, and standard deviation.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
81) The local amusement park was interested in the average wait time at their most popular roller
coaster at the peak park time (2 p.m.). They selected 13 patrons and had them get in line between
2 and 3 p.m. Each was given a stopwatch to record the time they spent in line. The times
recorded were as follows (in minutes; mean = 114.15):
118, 124, 108, 116, 99, 120, 148, 118, 119, 121, 45, 130, 118.
What is the range?
A) 103
B) 23.62
C) 557.97
D) 128.8
E) 115
Answer: A
Explanation: Range = largest value − smallest value = 148 − 45 = 103
Difficulty: 1 Easy
Topic: Measures of Variation
Learning Objective: 03-02 Compute and interpret the range, variance, and standard deviation.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
160
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82) The local amusement park was interested in the average wait time at their most popular roller
coaster at the peak park time (2 p.m.). They selected 13 patrons and had them get in line between
2 and 3 p.m. Each was given a stopwatch to record the time they spent in line. The times
recorded were as follows (in minutes; mean = 114.15):
118, 124, 108, 116, 99, 120, 148, 118, 119, 121, 45, 130, 118.
What is the variance?
A) 103
B) 23.62
C) 557.97
D) 128.8
E) 115
Answer: C
Explanation: Variance = [Σ (x− mean)2]/(n − 1) = 6695.69/12 = 557.97
Difficulty: 2 Medium
Topic: Measures of Variation
Learning Objective: 03-02 Compute and interpret the range, variance, and standard deviation.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
83) The local amusement park was interested in the average wait time at their most popular roller
coaster at the peak park time (2 p.m.). They selected 13 patrons and had them get in line between
2 and 3 p.m. Each was given a stopwatch to record the time they spent in line. The times
recorded were as follows (in minutes; mean = 114.15):
118, 124, 108, 116, 99, 120, 148, 118, 119, 121, 45, 130, 118.
What is the standard deviation?
A) 103
B) 23.62
C) 557.97
D) 128.8
E) 115
Answer: B
Explanation:
Std Dev =
=
=
=
= 23.62
Difficulty: 2 Medium
Topic: Measures of Variation
Learning Objective: 03-02 Compute and interpret the range, variance, and standard deviation.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
161
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written consent of McGraw-Hill Education.
84) Quality control is an important issue at ACME Company, which manufactures light bulbs.
To test the life-hours of their light bulbs, they randomly sampled nine light bulbs and measured
how many hours they lasted (mean = 346.6).
378, 361, 350, 375, 200, 391, 375, 368, 321
What is the range?
A) 342.43
B) 3424.3
C) 58.5
D) 191
E) 10,609
Answer: D
Explanation: Range = largest value − smallest value = 391 − 200 = 191
Difficulty: 1 Easy
Topic: Measures of Variation
Learning Objective: 03-02 Compute and interpret the range, variance, and standard deviation.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
85) Quality control is an important issue at ACME Company, which manufactures light bulbs.
To test the life hours of their light bulbs, they randomly sampled nine light bulbs and measured
how many hours they lasted (mean = 346.6).
378, 361, 350, 375, 200, 391, 375, 368, 321
What is the variance?
A) 342.43
B) 3424.3
C) 58.5
D) 191
E) 10,609
Answer: B
Explanation: Variance = [Σ (x− mean)2]/(n − 1) = 27,394.24/8 = 3424.28
Difficulty: 2 Medium
Topic: Measures of Variation
Learning Objective: 03-02 Compute and interpret the range, variance, and standard deviation.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
162
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written consent of McGraw-Hill Education.
86) Quality control is an important issue at ACME Company, which manufactures light bulbs.
To test the life-hours of their light bulbs, they randomly sampled nine light bulbs and measured
how many hours they lasted (mean = 346.6).
378, 361, 350, 375, 200, 391, 375, 368, 321
What is the standard deviation?
A) 342.43
B) 3424.3
C) 58.5
D) 191
E) 10,609
Answer: C
Explanation:
Std Dev =
=
=
=
= 58.5
Difficulty: 2 Medium
Topic: Measures of Variation
Learning Objective: 03-02 Compute and interpret the range, variance, and standard deviation.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
87) In a statistics class, 10 scores were randomly selected, with the following results: 74, 73, 77,
77, 71, 68, 65, 77, 67, 66.
What is the 90th percentile?
A) 77
B) 73
C) 74
D) 67
E) 65.9
Answer: A
Explanation: 65, 66, 67, 68, 71, 73, 74, 77, 77, 77
(90/100)n = (90/100)(10) = 9th position = 77
Difficulty: 2 Medium
Topic: Percentiles, Quartiles, and Box-and-Whisker Displays
Learning Objective: 03-04 Compute and interpret percentiles, quartiles, and box-and-whiskers
displays.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
163
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written consent of McGraw-Hill Education.
88) In a statistics class, 10 scores were randomly selected with the following results: 74, 73, 77,
77, 71, 68, 65, 77, 67, 66.
What is the third quartile?
A) 65.9
B) 67.3
C) 66.75
D) 73.85
E) 77.0
Answer: E
Explanation: 65, 66, 67, 68, 71, 73, 74, 77, 77, 77
(75/100)n = (75/100)(10) = 7.5th position so round up to 8 = 77
Difficulty: 2 Medium
Topic: Percentiles, Quartiles, and Box-and-Whisker Displays
Learning Objective: 03-04 Compute and interpret percentiles, quartiles, and box-and-whiskers
displays.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
89) In a statistics class, 10 scores were randomly selected with the following results: 74, 73, 77,
77, 71, 68, 65, 77, 67, 66.
What is the first quartile?
A) 65.9
B) 67.3
C) 67.0
D) 73.85
E) 77.0
Answer: C
Explanation: 65, 66, 67, 68, 71, 73, 74, 77, 77, 77
(25/100)n = (25/100)(10) = 2.5th position so round up to 3 = 67
Difficulty: 2 Medium
Topic: Percentiles, Quartiles, and Box-and-Whisker Displays
Learning Objective: 03-04 Compute and interpret percentiles, quartiles, and box-and-whiskers
displays.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
164
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written consent of McGraw-Hill Education.
90) In a statistics class, 10 scores were randomly selected, with the following results: 74, 73, 77,
77, 71, 68, 65, 77, 67, 66.
What is the 10th percentile?
A) 65.5
B) 67.3
C) 66.75
D) 73.85
E) 77.0
Answer: A
Explanation: 65, 66, 67, 68, 71, 73, 74, 77, 77, 77
(10/100)n = (10/100)(10) = 1st position = 65 + 66 / 2 = 65.5
Difficulty: 2 Medium
Topic: Percentiles, Quartiles, and Box-and-Whisker Displays
Learning Objective: 03-04 Compute and interpret percentiles, quartiles, and box-and-whiskers
displays.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
91) In a statistics class, 10 scores were randomly selected with the following results: 74, 73, 77,
77, 71, 68, 65, 77, 67, 66.
What is the 65th percentile?
A) 65.5
B) 67.3
C) 66.75
D) 74.0
E) 77.0
Answer: D
Explanation: 65, 66, 67, 68, 71, 73, 74, 77, 77, 77
(65/100)n = (65/100)(10) = 6.5th position, so round up to 7 = 74
Difficulty: 3 Hard
Topic: Percentiles, Quartiles, and Box-and-Whisker Displays
Learning Objective: 03-04 Compute and interpret percentiles, quartiles, and box-and-whiskers
displays.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
165
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written consent of McGraw-Hill Education.
92) In a statistics class, 10 scores were randomly selected with the following results: 74, 73, 77,
77, 71, 68, 65, 77, 67, 66.
What is the IQR?
A) 12.00
B) 5.25
C) 10
D) 5.00
E) 11.00
Answer: C
Explanation: IQR = Q3− Q1 = 77 − 67 = 10
Difficulty: 2 Medium
Topic: Percentiles, Quartiles, and Box-and-Whisker Displays
Learning Objective: 03-04 Compute and interpret percentiles, quartiles, and box-and-whiskers
displays.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
93) In a statistics class, 10 scores were randomly selected with the following results: 74, 73, 77,
77, 71, 68, 65, 77, 67, 66.
What are the lower and upper limits of a box-and-whiskers display of this data?
A) 67, 77
B) 57, 87
C) 37, 107
D) 52, 92
E) 47, 97
Answer: D
Explanation: Lower limit: Q1− 1.5 IQR = 67 − 15 = 52.
Upper limit: Q3 + 1.5 IQR = 77 + 15 = 92.
Difficulty: 3 Hard
Topic: Percentiles, Quartiles, and Box-and-Whisker Displays
Learning Objective: 03-04 Compute and interpret percentiles, quartiles, and box-and-whiskers
displays.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
166
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written consent of McGraw-Hill Education.
94) The company financial officer was interested in the average cost of PCs that had been
purchased in the past six months. She took a random sample of the price of 10 computers, with
the following results.
$3,250, $1,127, $2,995, $3,250, $3,445, $3,449, $1,482, $6,120, $3,009, $4,000
What is the 90th percentile?
A) $1,446.50
B) $3,449.00
C) $3,415.75
D) $4,000.00
E) $5,060.00
Answer: E
Explanation: Place scores in ascending order and calculate the index = (p/100)n = (90/100) × 10
= 9. When the index is an integer, take the average of the i and i+1 values: (4000 + 6120)/2 =
$5060.
Difficulty: 2 Medium
Topic: Percentiles, Quartiles, and Box-and-Whisker Displays
Learning Objective: 03-04 Compute and interpret percentiles, quartiles, and box-and-whiskers
displays.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
95) The company financial officer was interested in the average cost of PCs that had been
purchased in the past six months. She took a random sample of the price of 10 computers, with
the following results.
$3,250, $1,127, $2,995, $3,250, $3,445, $3,449, $1,482, $6,120, $3,009, $4,000
What is the third quartile?
A) $1,446.50
B) $2,617.00
C) $3,415.75
D) $3,449.00
E) $4,212.00
Answer: D
Explanation: Place scores in ascending order and calculate the index = (p/100)n = (75/100) × 10
= 7.5. When the index is not an integer, round up to the next integer to obtain the index value:
7.5 rounds to 8; the eighth value is $3,449.
Difficulty: 2 Medium
Topic: Percentiles, Quartiles, and Box-and-Whisker Displays
Learning Objective: 03-04 Compute and interpret percentiles, quartiles, and box-and-whiskers
displays.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
96) The company financial officer was interested in the average cost of PCs that had been
167
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written consent of McGraw-Hill Education.
purchased in the past six months. She took a random sample of the price of 10 computers, with
the following results.
$3,250, $1,127, $2,995, $3,250, $3,445, $3,449, $1,482, $6,120, $3,009, $4,000
What is the first quartile?
A) $1,446.50
B) $2,995.00
C) $3,415.75
D) $3,587.00
E) $4,212.00
Answer: B
Explanation: Place scores in ascending order and calculate the index = (p/100)n = (25/100) × 10
= 2.5. When the index is not an integer, round up to the next integer to obtain the index value:
2.5 rounds to 3; the third value is $2,995.
Difficulty: 2 Medium
Topic: Percentiles, Quartiles, and Box-and-Whisker Displays
Learning Objective: 03-04 Compute and interpret percentiles, quartiles, and box-and-whiskers
displays.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
97) The company financial officer was interested in the average cost of PCs that had been
purchased in the past six months. She took a random sample of the price of 10 computers, with
the following results.
$3,250, $1,127, $2,995, $3,250, $3,445, $3,449, $1,482, $6,120, $3,009, $4,000
What is the 10th percentile?
A) $1,304.50
B) $2,617.00
C) $3,415.75
D) $3,587.00
E) $4,212.00
Answer: A
Explanation: Place scores in ascending order and calculate the index = (p/100)n = (10/100) × 10
= 1. When the index is an integer, take the average of the i and i+1 values: (1127 + 1482)/2 =
1304.5.
Difficulty: 2 Medium
Topic: Percentiles, Quartiles, and Box-and-Whisker Displays
Learning Objective: 03-04 Compute and interpret percentiles, quartiles, and box-and-whiskers
displays.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
98) The company financial officer was interested in the average cost of PCs that had been
purchased in the past six months. She took a random sample of the price of 10 computers, with
168
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written consent of McGraw-Hill Education.
the following results.
$3,250, $1,127, $2,995, $3,250, $3,445, $3,449, $1,482, $6,120, $3,009, $4,000
What is the 65th percentile?
A) $1,446.50
B) $2,617.00
C) $3,445.00
D) $3,587.00
E) $4,212.00
Answer: C
Explanation: Place scores in ascending order and calculate the index = (p/100)n = (65/100) × 10
= 6.5. When the index is not an integer, round up to the next integer to obtain the index value:
6.5 rounds to 7; the seventh value is 3445.
Difficulty: 3 Hard
Topic: Percentiles, Quartiles, and Box-and-Whisker Displays
Learning Objective: 03-04 Compute and interpret percentiles, quartiles, and box-and-whiskers
displays.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
99) The company financial officer was interested in the average cost of PCs that had been
purchased in the past six months. She took a random sample of the price of 10 computers, with
the following results.
$3,250, $1,127, $2,995, $3,250, $3,445, $3,449, $1,482, $6,120, $3,009, $4,000
What is the IQR?
A) 681
B) 454
C) 1362
D) 255
E) 6120
Answer: B
Explanation: IQR = Q3− Q1 = 3449 − 2995 = 454
Difficulty: 2 Medium
Topic: Percentiles, Quartiles, and Box-and-Whisker Displays
Learning Objective: 03-04 Compute and interpret percentiles, quartiles, and box-and-whiskers
displays.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
169
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written consent of McGraw-Hill Education.
100) The company financial officer was interested in the average cost of PCs that had been
purchased in the past six months. She took a random sample of the price of 10 computers, with
the following results.
$3,250, $1,127, $2,995, $3,250, $3,445, $3,449, $1,482, $6,120, $3,009, $4,000
What are the lower and upper limits of a box-and-whiskers display of this data?
A) 2541, 3903
B) 2768, 3676
C) 2087, 4357
D) 2314, 4130
E) 1633, 2087
Answer: D
Explanation: Lower limit = Q1 − 1.5 IQR = 2995 − (1.5 × 454) = 2314
Upper limit = Q3 + 1.5 IQR = 3449 + (1.5 × 454) = 4130
Difficulty: 3 Hard
Topic: Percentiles, Quartiles, and Box-and-Whisker Displays
Learning Objective: 03-04 Compute and interpret percentiles, quartiles, and box-and-whiskers
displays.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
101) The local amusement park was interested in the average wait time at their most popular
roller coaster at the peak park time (2 p.m.). They selected 13 patrons and had them get in line
between 2 and 3 p.m. Each was given a stopwatch to record the time they spent in line. The times
recorded were as follows (in minutes).
118, 124, 108, 116, 99, 120, 148, 118, 119, 121, 45, 130, 118
What is the 90th percentile?
A) 100.8
B) 118
C) 130
D) 112
E) 45
Answer: C
Explanation: Place scores in ascending order and calculate the index = (p/100)n = (90/100) × 13
= 11.7. When the index is not an integer, round up to the next integer to obtain the index value:
11.7 rounds to 12; the 12th value is 130.
Difficulty: 2 Medium
Topic: Percentiles, Quartiles, and Box-and-Whisker Displays
Learning Objective: 03-04 Compute and interpret percentiles, quartiles, and box-and-whiskers
displays.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
170
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written consent of McGraw-Hill Education.
102) The local amusement park was interested in the average wait time at their most popular
roller coaster at the peak park time (2 p.m.). They selected 13 patrons and had them get in line
between 2 and 3 p.m. Each was given a stopwatch to record the time they spent in line. The times
recorded were as follows (in minutes).
118, 124, 108, 116, 99, 120, 148, 118, 119, 121, 45, 130, 118
What is the third quartile?
A) 100.8
B) 118
C) 130
D) 112
E) 121
Answer: E
Explanation:
Place scores in ascending order and calculate the index = (p/100)n = (75/100) × 13 = 9.75. When
the index is not an integer, round up to the next integer to obtain the index value: 9.75 rounds to
10; the 10th value is 121.
Difficulty: 2 Medium
Topic: Percentiles, Quartiles, and Box-and-Whisker Displays
Learning Objective: 03-04 Compute and interpret percentiles, quartiles, and box-and-whiskers
displays.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
171
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written consent of McGraw-Hill Education.
103) The local amusement park was interested in the average wait time at their most popular
roller coaster at the peak park time (2 p.m.). They selected 13 patrons and had them get in line
between 2 and 3 p.m. Each was given a stopwatch to record the time they spent in line. The times
recorded were as follows (in minutes).
118, 124, 108, 116, 99, 120, 148, 118, 119, 121, 45, 130, 118
What is the first quartile?
A) 100.8
B) 118
C) 130
D) 116
E) 45
Answer: D
Explanation:
Place scores in ascending order and calculate the index = (p/100)n = (25/100) × 13 = 3.25. When
the index is not an integer, round up to the next integer to obtain the index value: 3.25 rounds to
4; the fourth value is 116.
Difficulty: 2 Medium
Topic: Percentiles, Quartiles, and Box-and-Whisker Displays
Learning Objective: 03-04 Compute and interpret percentiles, quartiles, and box-and-whiskers
displays.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
172
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written consent of McGraw-Hill Education.
104) The local amusement park was interested in the average wait time at their most popular
roller coaster at the peak park time (2 p.m.). They selected 13 patrons and had them get in line
between 2 and 3 p.m. Each was given a stopwatch to record the time they spent in line. The times
recorded were as follows (in minutes).
118, 124, 108, 116, 99, 120, 148, 118, 119, 121, 45, 130, 118
What is the 10th percentile?
A) 99
B) 120
C) 130
D) 112
E) 45
Answer: A
Explanation:
Place scores in ascending order and calculate the index = (p/100)n = (10/100) × 13 = 1.3. When
the index is not an integer, round up to the next integer to obtain the index value: 1.3 rounds to 2;
the second value is 99.
Difficulty: 2 Medium
Topic: Percentiles, Quartiles, and Box-and-Whisker Displays
Learning Objective: 03-04 Compute and interpret percentiles, quartiles, and box-and-whiskers
displays.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
173
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written consent of McGraw-Hill Education.
105) The local amusement park was interested in the average wait time at their most popular
roller coaster at the peak park time (2 p.m.). They selected 13 patrons and had them get in line
between 2 and 3 p.m. Each was given a stopwatch to record the time they spent in line. The times
recorded were as follows (in minutes).
118, 124, 108, 116, 99, 120, 148, 118, 119, 121, 45, 130, 118
What is the 65th percentile?
A) 99
B) 120
C) 130
D) 112
E) 45
Answer: B
Explanation: Place scores in ascending order and calculate the index = (p/100)n = (65/100) × 13
= 8.45. When the index is not an integer, round up to the next integer to obtain the index value:
8.45 rounds to 9; the ninth value is 120.
Difficulty: 3 Hard
Topic: Percentiles, Quartiles, and Box-and-Whisker Displays
Learning Objective: 03-04 Compute and interpret percentiles, quartiles, and box-and-whiskers
displays.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
106) The local amusement park was interested in the average wait time at their most popular
roller coaster at the peak park time (2 p.m.). They selected 13 patrons and had them get in line
between 2 and 3 p.m. Each was given a stopwatch to record the time they spent in line. The times
recorded were as follows (in minutes).
118, 124, 108, 116, 99, 120, 148, 118, 119, 121, 45, 130, 118
What is the IQR?
A) 103
B) 5
C) 28
D) 30
E) 7
Answer: B
Explanation: IQR = Q3 − Q1 = 121 − 116 = 5
Difficulty: 2 Medium
Topic: Percentiles, Quartiles, and Box-and-Whisker Displays
Learning Objective: 03-04 Compute and interpret percentiles, quartiles, and box-and-whiskers
displays.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
174
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written consent of McGraw-Hill Education.
107) The local amusement park was interested in the average wait time at their most popular
roller coaster at the peak park time (2 p.m.). They selected 13 patrons and had them get in line
between 2 and 3 p.m. Each was given a stopwatch to record the time they spent in line. The times
recorded were as follows (in minutes).
118, 124, 108, 116, 99, 120, 148, 118, 119, 121, 45, 130, 118
What are the lower and upper limits of a box-and-whiskers display of this data?
A) 80.5, 154.00
B) 108.5, 128.5
C) 127.75, 138.25
D) 143.50, 154.00
E) 15.75, 31.50
Answer: B
Explanation: Lower limit: Q1 − 1.5 IQR; upper limit: Q3 + 1.5 IQR; 116 − (1.5 × 5) = 108.5 for
the lower limit, and 121 + (1.5 × 5) = 128.5 for the upper limit.
Difficulty: 3 Hard
Topic: Percentiles, Quartiles, and Box-and-Whisker Displays
Learning Objective: 03-04 Compute and interpret percentiles, quartiles, and box-and-whiskers
displays.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
108) Compute the population variance of these data: 16, 18, 23, 21, 17, 16, 24, 23, 9, 17, 11, 16,
22, 10, 15, 14.
A) 21.9
B) 3.87
C) 20.5
D) 17.0
E) 3.625
Answer: C
Explanation:
=
=
=
= 20.5
Difficulty: 2 Medium
Topic: Measures of Variation
Learning Objective: 03-02 Compute and interpret the range, variance, and standard deviation.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
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written consent of McGraw-Hill Education.
109) If the median of a data set is 760, the third quartile is 950, and the first quartile is 650, what
is the interquartile range?
A) 300
B) 190
C) 110
D) 150
E) 910
Answer: A
Explanation: Interquartile range = 950 − 650 = 300
Difficulty: 2 Medium
Topic: Percentiles, Quartiles, and Box-and-Whisker Displays
Learning Objective: 03-04 Compute and interpret percentiles, quartiles, and box-and-whiskers
displays.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
110) Compute the sample standard deviation of the data set 6, 4, 2, 1, 4, 1.
A) 1.83
B) 2.00
C) 1.41
D) 3.33
E) 4.00
Answer: B
Explanation: Std Dev =
=
; mean = 3;
=
=2
Difficulty: 2 Medium
Topic: Measures of Variation
Learning Objective: 03-02 Compute and interpret the range, variance, and standard deviation.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
176
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written consent of McGraw-Hill Education.
111) The average lateness for one of the top airline companies is 10 minutes. The variance of the
lateness measure is calculated as 9. An airplane arrived 13 minutes after the stated arrival time.
Calculate the z-score for the lateness of this particular airplane.
A) .33
B) .58
C) 1.33
D) .44
E) 1.00
Answer: E
Explanation:
Z=
=1
Difficulty: 2 Medium
Topic: Measures of Variation
Learning Objective: 03-02 Compute and interpret the range, variance, and standard deviation.
Bloom's: Apply
AACSB: Analytical Thinking
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112) The average life of Canadian women is 73.75 years, and the standard deviation of the life
expectancy of Canadian women is 6.5 years. Using Chebyshev's theorem, determine the
minimum percentage of women in Canada whose life expectancy is between 64 and 83.5 years.
A) 93.17%
B) 68.26%
C) 55.56%
D) 88.89%
E) 33.33%
Answer: C
Explanation: Determine the value of k: (83.5, 64) = 73.75 ± k(6.5); k = 1.5
1 − (1/k2) = 1 − (1/2.25) = .5556, or 55.56%
Difficulty: 3 Hard
Topic: Measures of Variation
Learning Objective: 03-03 Use the Empirical Rule and Chebyshev's Theorem to describe
variation.
Bloom's: Apply
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177
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113) The average life of Canadian women is 73.75 years, and the standard deviation of the life
expectancy of Canadian women is 6.5 years. Based on Chebyshev's theorem, determine the
upper and lower bounds on the average life expectancy of Canadian women such that at least 90
percent of the population is included.
A) [12.09 135.41]
B) [8.75 138.75]
C) [53.20 94.30]
D) [66.38 81.13]
E) [67.25 80.25]
Answer: C
Explanation:
1−
= .90
= .1
k2 =
= 10; k =
= 3.162
lower bound = 73.75 − (3.162)(6.5) = 53.2
upper bound = 73.75 + (3.162)(6.5) = 94.3
Difficulty: 3 Hard
Topic: Measures of Variation
Learning Objective: 03-03 Use the Empirical Rule and Chebyshev's Theorem to describe
variation.
Bloom's: Apply
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178
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written consent of McGraw-Hill Education.
114) The following table shows the Price-to-Earnings ratio for a stereo equipment manufacturing
company between 1998 and 2002.
Year
1998
1999
2000
2001
2002
P/E Ratio
12.4
14.6
11.1
8.2
6.8
Determine the percentage change in the P/E ratios from 1998 to 1999.
A) 15.07%
B) 17.74%
C) 20.72%
D) −17.74%
E) −15.07%
Answer: B
Explanation:
1=
× 100 = 17.74%
Difficulty: 2 Medium
Topic: Geometric Mean
Learning Objective: 03-07 Compute and interpret the geometric mean.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
179
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written consent of McGraw-Hill Education.
115) The following table shows the Price-to-Earnings ratio for a stereo equipment manufacturing
company between 1998 and 2002.
Year
1998
1999
2000
2001
2002
P/E Ratio
12.4
14.6
11.1
8.2
6.8
Determine the percentage change in the P/E ratios from 1999 to 2000.
A) 23.97%
B) 31.53%
C) 27.26%
D) −31.53%
E) −23.97%
Answer: E
Explanation:
R2 =
× 100 = -23.97%
Difficulty: 2 Medium
Topic: Geometric Mean
Learning Objective: 03-07 Compute and interpret the geometric mean.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
180
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written consent of McGraw-Hill Education.
116) The following table shows the Price-to-Earnings ratio for a stereo equipment manufacturing
company between 1998 and 2002. The annual percentage growth rate of the P/E ratios is also
calculated and given below.
Year
1998
1999
2000
2001
2002
P/E Ratio
12.4
14.6
11.1
8.2
6.8
Growth Rate (%)
17.74 (1998-1999)
-23.97 (1999-2000)
-26.13 (2000-2001)
-17.07 (2001-2002)
Calculate the geometric mean growth rate increase or decrease over the period from 1998 to
2002.
A) −.2592
B) −.1395
C) −.1816
D) .8616
E) .7417
Answer: B
Explanation:
Rg =
−1
Rg = (
) − 1 = −.1397
Difficulty: 2 Medium
Topic: Geometric Mean
Learning Objective: 03-07 Compute and interpret the geometric mean.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
181
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written consent of McGraw-Hill Education.
117) Suppose that a company's annual sales were $1,200,000 in 1999. The annual growth rate of
sales from 1999 to 2000 was 16 percent, from 2000 to 2001 it was −5 percent, and from 2001 to
2002 it was 22 percent.
What is the geometric mean growth rate of sales over this three-year period?
A) 7.68%
B) 9.27%
C) 10.37%
D) 11.00%
E) 14.33%
Answer: C
Explanation: Forecasted Sales = 1,200,000(1 + .1037)5 = 1,965,337
Difficulty: 2 Medium
Topic: Geometric Mean
Learning Objective: 03-07 Compute and interpret the geometric mean.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
182
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written consent of McGraw-Hill Education.
118) The following frequency table summarizes the ages of 60 shoppers at the local grocery
store.
Age of the
Shopper
15-23
24-32
33-41
42-50
51-59
60-68
Frequency
10
21
10
8
5
6
The sample mean for the above frequency table is calculated as 36.25. Calculate the approximate
sample standard deviation for this data set.
A) 192.49
B) 195.75
C) 26.83
D) 13.87
E) 13.99
Answer: E
Explanation:
Class Midpoint
(Mi)
19
28
37
46
55
64
s2 =
Mi-X
−17.25
−8.25
.75
9.75
18.75
27.75
(Mi-X)2
297.5625
68.0625
.5625
95.0625
351.5625
770.0625
FiMi-X2
2,975.63
1,429.31
5.63
76.05
1,757.81
4,620.38
10,864.81
≅ 184.149
s=
= 13.57 years
Difficulty: 2 Medium
Topic: Weighted Means and Grouped Data
Learning Objective: 03-06 Compute and interpret weighted means and the mean standard
deviation of grouped data.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
183
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written consent of McGraw-Hill Education.
119) Personnel managers usually want to know where a job applicant ranked in his or her
graduating class. With a grade point average of 3.83, Michelle Robinson graduated above the
93rd percentile of her graduating class. What is the percentile rank of a student whose GPA was
the median GPA?
A) 25th
B) 50th
C) 75th
D) 10th
E) 93rd
Answer: B
Explanation: Median is the equivalent of the 50th percentile.
Difficulty: 1 Easy
Topic: Percentiles, Quartiles, and Box-and-Whisker Displays
Learning Objective: 03-04 Compute and interpret percentiles, quartiles, and box-and-whiskers
displays.
Bloom's: Apply
AACSB: Analytical Thinking
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184
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written consent of McGraw-Hill Education.
120) The Rivertown city council is attempting to choose one of four sites (A, B, C, or D) as the
location for its new emergency facility. After the new emergency facility becomes available for
service, the current emergency facility will be shut down. The project manager has estimated the
following response times in minutes from each of the proposed sites to the four areas that must
be served by the emergency facility.
Proposed Site
A
B
C
D
Area Served
2
3
4.4
3.6
7.4
3.4
5.9
5.9
4.8
6.5
1
5.2
6.0
5.8
4.3
4
6.5
4.0
5.8
5.1
The number of emergency runs from the current emergency facility to each of the four areas over
the past year is as follows:
Area
Number of runs
1
150
2
65
3
175
4
92
Compute the weighted mean response time from the proposed locations and determine which
proposed site should be selected for the new emergency facility.
A) site A
B) site B
C) site C
D) site D
Answer: A
Explanation: mA = 4.76; mB = 4.86; mC = 5.85; mD = 5.32. Choose site A.
Difficulty: 3 Hard
Topic: Weighted Means and Grouped Data
Learning Objective: 03-06 Compute and interpret weighted means and the mean standard
deviation of grouped data.
Bloom's: Apply; Analyze
AACSB: Analytical Thinking
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185
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written consent of McGraw-Hill Education.
121) Researchers wish to study fuel consumption rates based on speed. The data from the test car
at 10 speeds are below.
Speed
15
23
30
35
42
45
50
54
60
65
Miles/Gallon
14
17
20
24
26
23
18
15
60
10
It can be shown that for these data:
= 41.9, = 17.8,
= 2352.9,
= 267.6,
(
- ) = −270.2.
Calculate the sample covariance.
A) −270.2
B) −30.02
C) −27.02
D) −74.58
E) −82.86
Answer: B
Explanation:
sxy =
= −270.2 / 9 = −30.02
Difficulty: 3 Hard
Topic: Covariance, Correlation, and the Least Squares Line
Learning Objective: 03-05 Compute and interpret covariance, correlation, and the least squares
line.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
186
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written consent of McGraw-Hill Education.
122) Researchers wish to study fuel consumption rates based on speed. The data from the test car
at 10 speeds are below.
Speed
15
23
30
35
42
45
50
54
60
65
Miles/Gallon
14
17
20
24
26
23
18
15
60
10
It can be shown that for these data:
= 41.9, = 17.8,
= 2352.9,
= 267.6,
(
− ) = −270.2.
Calculate b1.
Answer: −0.1148
=
=
(
− ) /(n − 1) = -270.2 /9 = −30.02
/(n − 1) = 2352.9) /9 = 261.43
b1 = -30.02/261.43 = −0.1148
Difficulty: 3 Hard
Topic: Covariance, Correlation, and the Least Squares Line
Learning Objective: 03-05 Compute and interpret covariance, correlation, and the least squares
line.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
187
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written consent of McGraw-Hill Education.
123) Researchers wish to study fuel consumption rates based on speed. The data from 10 cars are
below.
Speed
15
23
30
35
42
45
50
54
60
65
Miles/Gallon
14
17
20
24
26
23
18
15
60
10
It can be shown that for these data:
= 41.9, = 17.8,
= 2352.9,
= 267.6,
(
− ) = −270.2.
Calculate the sample correlation coefficient.
A) .12
B) −.12
C) −.36
D) −.34
E) .34
Answer: D
Explanation: r = sxy/(sx sy) = −30.02/88.17 = −.34
Difficulty: 3 Hard
Topic: Covariance, Correlation, and the Least Squares Line
Learning Objective: 03-05 Compute and interpret covariance, correlation, and the least squares
line.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
188
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written consent of McGraw-Hill Education.
124) In a study of the factors that affect success in economics, data were collected for 8 business
students. Scores on a calculus placement test are given with economics final exam scores. The
data are below:
Calculus Placement Score
17
21
11
16
15
11
24
27
Exam Final Score
73
66
64
61
70
71
90
68
It can be shown that for these data:
= 17.75, = 70.38,
= 237.50,
= 545.875,
(
− )=
140.75.
Calculate the sample covariance.
A) 140.75
B) 77.98
C) 33.93
D) 20.11
E) 17.59
Answer: D
Explanation:
=
(
− ) /(n − 1) = 140.75 /7 = 20.11
Difficulty: 3 Hard
Topic: Covariance, Correlation, and the Least Squares Line
Learning Objective: 03-05 Compute and interpret covariance, correlation, and the least squares
line.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
189
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written consent of McGraw-Hill Education.
125) In a study of the factors that affect success in economics, data were collected for 8 business
students. Scores on a calculus placement test are given with economics final exam scores. The
data are below.
Calculus Placement Score
17
21
11
16
15
11
24
27
Exam Final Score
73
66
64
61
70
71
90
68
It can be shown that for these data:
= 17.75, = 70.38,
= 237.50,
= 545.875,
(
− )=
140.75.
Calculate the sample correlation coefficient.
A) .15
B) .11
C) .39
D) −.39
E) −.11
Answer: C
Explanation:
− ) /(n − 1) = 140.75 /7 = 20.11
=
(
=
/ (n − 1) = 237.50 /7 = 33.93
b1 = 20.11/33.93 = .593
Difficulty: 3 Hard
Topic: Covariance, Correlation, and the Least Squares Line
Learning Objective: 03-05 Compute and interpret covariance, correlation, and the least squares
line.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
190
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written consent of McGraw-Hill Education.
126) In a study of the factors that affect success in economics, data were collected for 8 business
students. Scores on a calculus placement test are given with economics final exam scores. The
data are below.
Calculus Placement Score
17
21
11
16
15
11
24
27
Exam Final Score
73
66
64
61
70
71
90
68
It can be shown that for these data:
= 17.75, = 70.38,
= 237.50,
= 545.875,
(
− )=
140.75.
Calculate b1.
A) .15
B) .26
C) .59
D) −.59
E) −.26
Answer: C
Explanation: r = Sxy /(Sx × Sy) = 20.11/51.44 = .39
Difficulty: 3 Hard
Topic: Covariance, Correlation, and the Least Squares Line
Learning Objective: 03-05 Compute and interpret covariance, correlation, and the least squares
line.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
191
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written consent of McGraw-Hill Education.
127) In a study of employee stock ownership plans, data were collected at seven companies on
satisfaction with the plan and the amount of organization commitment.
Satisfaction
5.05
4.12
5.39
4.17
4.00
4.49
5.40
Commitment
5.37
4.49
5.42
4.45
4.24
5.34
5.62
It can be shown that for these data
= 4.66, = 4.99,
= 2.23,
= 1.95,
(
− ) = 1.898.
Calculate b1.
Answer: .851
− ) /(n − 1) = 1.898/6 = .3164
=
(
=
/ (n − 1) = 2.23/6 = .372
b1 = .3164/.372 = .851
Difficulty: 3 Hard
Topic: Covariance, Correlation, and the Least Squares Line
Learning Objective: 03-05 Compute and interpret covariance, correlation, and the least squares
line.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
192
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written consent of McGraw-Hill Education.
128) In an analysis of the relationship between the average weekly temperature in a major city
and the per person consumption of ice cream (pints), a least squares line is defined by the
equation 5.72 + .004x. Predict the average amount of ice cream consumed when it is 50° outside.
Answer: 5.92 pints
y = 5.72 + .004(50) = 5.92
Difficulty: 1 Easy
Topic: Covariance, Correlation, and the Least Squares Line
Learning Objective: 03-05 Compute and interpret covariance, correlation, and the least squares
line.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
129) From the following table of values and corresponding sample sizes, calculate the weighted
mean.
Group
1
2
3
4
5
X
3.1
5.1
4.2
2.5
4.8
n
9
7
10
2
6
Answer: 4.1
(3.1 × 9 + 5.1 × 7 + 4.2 × 10 + 2.5 × 2 + 4.8 × 6)/34 = 139.4/34 = 4.1
Difficulty: 2 Medium
Topic: Weighted Means and Grouped Data
Learning Objective: 03-06 Compute and interpret weighted means and the mean standard
deviation of grouped data.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
193
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written consent of McGraw-Hill Education.
130) Using grouped data of 14 classes with a sample mean of 51 and a sample variance of 6.42,
calculate the group sampled standard deviation.
Answer: 2.53
= 2.53
Difficulty: 1 Easy
Topic: Weighted Means and Grouped Data
Learning Objective: 03-06 Compute and interpret weighted means and the mean standard
deviation of grouped data.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
131) A random sample of 60 students in the business statistics course answered a survey on the
average number of hours they spent on statistics each week. Unfortunately, the original data were
lost and all that remains is the frequency table below. From these data, calculate the estimated
sample mean.
Class
1
2
3
4
5
Hrs
0-3
4-7
8-11
12-15
16-19
N
18
16
14
10
2
Hrs
0-3
4-7
8-11
12-15
16-19
N
18
16
14
10
2
60
Answer: 6.97
Class
1
2
3
4
5
Midpt
1.5
5.5
9.5
13.5
17.5
fM
27
88
133
135
35
418
6.97
Difficulty: 2 Medium
Topic: Weighted Means and Grouped Data
Learning Objective: 03-06 Compute and interpret weighted means and the mean standard
deviation of grouped data.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
194
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written consent of McGraw-Hill Education.
132) A random sample of 60 students in the business statistics course answered a survey on the
average number of hours they spent on statistics each week. Unfortunately, the original data were
lost and all that remains is the frequency table below. From these data, calculate the estimated
sample standard deviation.
Class
1
2
3
4
5
Hrs
0-3
4-7
8-11
12-15
16-19
N
18
16
14
10
2
60
Midpt
1.5
5.5
9.5
13.5
17.5
fM
27
88
133
135
35
418
fM
27
88
133
135
35
418
(M-μ)2
29.9209
2.1609
6.4009
42.6409
110.8809
Answer: 4.714
Class
1
2
3
4
5
Hrs
0-3
4-7
8-11
12-15
16-19
N
18
16
14
10
2
60
Midpt
1.5
5.5
9.5
13.5
17.5
f(M-μ)2
538.5762
34.5744
89.6126
426.409
221.7618
1310.934
Sample variance = (1310.934)/(n − 1) = 1310.934/59 = 22.21922
Sample standard deviation =
= 4.713727
Difficulty: 3 Hard
Topic: Weighted Means and Grouped Data
Learning Objective: 03-06 Compute and interpret weighted means and the mean standard
deviation of grouped data.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
195
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written consent of McGraw-Hill Education.
133) A real estate appraiser is gathering housing sales data by street in the neighborhood in
preparation for his next job. Listed below are the six streets and the average sales price and the
houses sold in the last 12 months. Calculate the mean sales price for the neighborhood.
Street
Elm
Maple
Oak
Pine
Rose
Petunia
Avg Sales Price
159,999
210,998
185,000
202,632
175,500
352,941
N
1
6
4
4
5
3
Answer: $213,602
Street
Elm
Maple
Oak
Pine
Rose
Petunia
Avg Sales Price
159,999
210,998
185,000
202,632
175,500
352,941
N
1
6
4
4
5
3
23
159,999
1,265,988
740,000
810,528
877,500
1,058,823
4,912,838
213,602
Difficulty: 2 Medium
Topic: Weighted Means and Grouped Data
Learning Objective: 03-06 Compute and interpret weighted means and the mean standard
deviation of grouped data.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
196
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written consent of McGraw-Hill Education.
134) A company CEO asked the marketing research department to find the average age of
consumers who bought the most profitable product made by the company. From survey data
gathered two years ago, the researchers found the following table. Calculate the average age to
give to the CEO.
Midpt of Age Class
17.5
23.5
29.5
35.5
41.5
52.5
N
65
100
220
250
120
85
Average age = 33.7
Answer:
Midpt of Age Class
17.5
23.5
29.5
35.5
41.5
52.5
N
65
100
220
250
120
85
840
1137.5
2350
6490
8875
4980
4462.5
28295
33.68452
Difficulty: 1 Easy
Topic: Weighted Means and Grouped Data
Learning Objective: 03-06 Compute and interpret weighted means and the mean standard
deviation of grouped data.
Bloom's: Apply
AACSB: Analytical Thinking
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197
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written consent of McGraw-Hill Education.
135) Find the weighted mean per capita income for the following random sample of six cities in
the Midwest.
City
A
B
C
D
E
F
Population
540,000
1,250,000
325,000
2,461,000
845,000
620,000
Per
Capita
Income
$ 26,338
$ 28,455
$ 36,574
$ 33,690
$ 31,998
$ 29,442
Answer: $31,432
City
A
B
C
D
E
F
Average
Population
540,000
1,250,000
325,000
2,461,000
845,000
620,000
6,041,000
Per
Capita
Income
$ 26,338
$ 28,455
$ 36,574
$ 33,690
$ 31,998
$ 29,442
31,432
$
$
$
$
$
$
$
14,222,520,000
35,568,750,000
11,886,550,000
82,911,090,000
27,038,310,000
18,254,040,000
189,881,260,000
Difficulty: 2 Medium
Topic: Weighted Means and Grouped Data
Learning Objective: 03-06 Compute and interpret weighted means and the mean standard
deviation of grouped data.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
198
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written consent of McGraw-Hill Education.
136) An initial investment of $10,000 is observed over 3 years with a geometric mean return at
the end of year 3 of .512. Determine the value of the investment after 3 years.
Answer: $34,566
$10,000 (1 + .512)3 = 10,000(3.4566) = 34,566
Difficulty: 2 Medium
Topic: Geometric Mean
Learning Objective: 03-07 Compute and interpret the geometric mean.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
137) An initial investment of $10,000 has a value of $7,382 at the end of year 1. What is the rate
of return for the first year?
Answer: −26.18%
R1 = ((7382 − 10,000)/10,000) = −2618/10,000 = −.2618 × 100 = −26.18%
Difficulty: 2 Medium
Topic: Geometric Mean
Learning Objective: 03-07 Compute and interpret the geometric mean.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
199
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written consent of McGraw-Hill Education.
138) An initial investment of $10,000 has a value of $7,382 at the end of year 1, a rate of return
of 62.43 percent for year 2, and a geometric mean return at the end of year 3 of .512. Determine
the rate of return for the third year.
Answer: 188.3% for R3
Rg = .512 = (3√(R1 + 1)(R2 + 1)(R3 + 1)) − 1
1.512 = (3√(R1 + 1)(R2 + 1)(R3 + 1))
1.512 = 3√(-.2618 + 1)(.6243 + 1)(R3 + 1)
3.457 = (1.199)(R3 + 1)
2.883 = R3 + 1
1.883 = R3
R3 = 1.883 × 100 = 188.3%
Difficulty: 3 Hard
Topic: Geometric Mean
Learning Objective: 03-07 Compute and interpret the geometric mean.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
139) At the end of 2007, the IRA owned by Joe Smith had a value of $1.2 million. With a rate of
return of −29.75 percent in 2008 and a rate of return of 2.98 percent in 2009, calculate the
geometric mean rate of return for the two-year period.
Answer: −.1495
Rg =
− 1 = −.1495
Difficulty: 2 Medium
Topic: Geometric Mean
Learning Objective: 03-07 Compute and interpret the geometric mean.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
200
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written consent of McGraw-Hill Education.
140) The geometric mean growth rate of sales for used cars in a geographic area from 2005 to
2009 was 16.42 percent. Annual sales in 2005 were $14.2 million. Find the ending value of sales
after this four-year period. (Round your answer to 2 decimal places.)
Answer: $26.09 million
14.2(1 + .1642)4 = 26.09
Difficulty: 2 Medium
Topic: Geometric Mean
Learning Objective: 03-07 Compute and interpret the geometric mean.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
141) Suppose that annual sales for a company were $3.6 million at the beginning of a three-year
period and at the end had increased to $6.1 million. Find the geometric growth rate of sales.
Answer: .19
3.6(1 + Rg)3 = 6.1
(1 + Rg)3 = 1.69
(1 + Rg) = 1.1911
Rg = .1911
Difficulty: 3 Hard
Topic: Geometric Mean
Learning Objective: 03-07 Compute and interpret the geometric mean.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
201
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written consent of McGraw-Hill Education.
142) The rate of return for each of the past four years on a market fund are R1 = 2.4%, R2 =
1.0%, R3 = −3.2%, and R4 = .5%. Find the geometric mean rate of return.
Answer: .0015
)−1
Rg = (
)−1
=(
= 1.0015 − 1 = .0015
Difficulty: 3 Hard
Topic: Geometric Mean
Learning Objective: 03-07 Compute and interpret the geometric mean.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
143) Following a factor analysis of 15 personality characteristic ratings of politicians by a
random sample of 40,000 registered voters, the following table of the first 7 factors and their
corresponding eigenvalues and percentage of explained variation was produced. Which factors
should an analyst choose when defining the characteristics of politicians?
Factor
Eigenvalue
1
2
3
4
5
6
7
7.504
2.062
1.468
1.209
.741
.484
.344
Percent of
Variation
50.0
13.7
9.8
8.1
4.9
3.2
2.3
Answer: Factors 1, 2, 3, and 4
Use factors that have an eigenvalue greater than 1.
Difficulty: 3 Hard
Topic: Factor Analysis
Learning Objective: 03-11 Interpret the information provided by factor analysis.
Bloom's: Apply
AACSB: Reflective Thinking; Analytical Thinking
Accessibility: Keyboard Navigation
202
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written consent of McGraw-Hill Education.
144) Interpret a lift ratio of .9259.
Answer: 7.41 percent of customers with similar patterns are less likely to follow
recommendation than a random customer.
A lift ratio is calculated by dividing confidence percentage by support percentage. The difference
from 1 is the percentage of a customer base that is or is not following recommendation from
association rules.
Difficulty: 3 Hard
Topic: Association Rules
Learning Objective: 03-08 Interpret the information provided by association rules.
Bloom's: Apply
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
145) Interpret a lift ratio of 1.111.
Answer: 11.1 percent of customers with similar patterns are more likely to follow
recommendation than a random customer.
A lift ratio is calculated by dividing confidence percentage by support percentage. The difference
from 1 is the percentage of a customer base that is or is not following recommendation from
association rules.
Difficulty: 3 Hard
Topic: Association Rules
Learning Objective: 03-08 Interpret the information provided by association rules.
Bloom's: Apply
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
203
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written consent of McGraw-Hill Education.
1) In any probability situation, either an event or its complement must occur.
Answer: TRUE
Explanation: The probability of the experiment is that only one of the outcomes will occur.
Difficulty: 2 Medium
Topic: Some Elementary Probability Rules
Learning Objective: 04-03 Use elementary probability rules to compute probabilities.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
2) An event is a collection of sample space outcomes.
Answer: TRUE
Explanation: It is also called experimental outcomes, and only one of these sample space
outcomes will occur on a single repetition of the experiment.
Difficulty: 1 Easy
Topic: Probability and Events
Learning Objective: 04-02 List the outcomes in a sample space and use the list to compute
probabilities.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
3) Two events are independent if the probability of one event is influenced by whether or not the
other event occurs.
Answer: FALSE
Explanation: Independence of events means there is no influence.
Difficulty: 2 Medium
Topic: Conditional Probability and Independence
Learning Objective: 04-04 Compute conditional probabilities and assess independence.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
204
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written consent of McGraw-Hill Education.
4) Mutually exclusive events have a nonempty intersection.
Answer: FALSE
Explanation: Mutually exclusive events do not intersect (have no sample spaces in common).
Difficulty: 2 Medium
Topic: Some Elementary Probability Rules
Learning Objective: 04-03 Use elementary probability rules to compute probabilities.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
5) A subjective probability is a probability assessment that is based on experience, intuitive
judgment, or expertise.
Answer: TRUE
Explanation: This means that an individual injects their opinion and thought into whether an
event is deemed a success or failure.
Difficulty: 2 Medium
Topic: Probability, Sample Spaces, and Probability Models
Learning Objective: 04-01 Define a probability, a sample space, and a probability model.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
6) The probability of an event is the sum of the probabilities of the sample space outcomes that
correspond to the event.
Answer: TRUE
Explanation: This helps us deal with the uncertainty of an event to determine the likelihood that
an event will occur.
Difficulty: 2 Medium
Topic: Probability and Events
Learning Objective: 04-02 List the outcomes in a sample space and use the list to compute
probabilities.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
205
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written consent of McGraw-Hill Education.
7) If events A and B are mutually exclusive, then P(A|B) is always equal to zero.
Answer: TRUE
Explanation: This means that either one or the other has to occur—they both cannot occur at the
same time.
Difficulty: 3 Hard
Topic: Some Elementary Probability Rules; Conditional Probability and Independence
Learning Objective: 04-03 Use elementary probability rules to compute probabilities.; 04-04
Compute conditional probabilities and assess independence.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
8) If events A and B are independent, then P(A|B) is always equal to zero.
Answer: FALSE
Explanation: If events A and B are independent, then P(A|B) is always equal to P(A).
Difficulty: 2 Medium
Topic: Conditional Probability and Independence
Learning Objective: 04-04 Compute conditional probabilities and assess independence.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
9) If events A and B are mutually exclusive, then P(A∩B) is always equal to zero.
Answer: TRUE
Explanation: They have no sample space outcomes in common.
Difficulty: 1 Easy
Topic: Some Elementary Probability Rules
Learning Objective: 04-03 Use elementary probability rules to compute probabilities.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
10) Events that have no sample space outcomes in common, and therefore cannot occur
simultaneously, are referred to as independent events.
Answer: FALSE
Explanation: This is a definition of mutually exclusive events.
Difficulty: 2 Medium
Topic: Conditional Probability and Independence
Learning Objective: 04-04 Compute conditional probabilities and assess independence.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
206
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written consent of McGraw-Hill Education.
11) The method of assigning probabilities when all outcomes are equally likely to occur is called
the classical method.
Answer: TRUE
Explanation: This is the classic example of toss a coin either heads or tails — logic says that
either outcome is equally as likely.
Difficulty: 1 Easy
Topic: Probability, Sample Spaces, and Probability Models
Learning Objective: 04-01 Define a probability, a sample space, and a probability model.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
12) Bayes' Theorem uses prior probabilities with additional information to compute posterior
probabilities.
Answer: TRUE
Explanation: The book gives the example of testing the entire population for HIV — and
because of the prior probabilities given one would not test the population for HIV because there
would be a high rate of false positives.
Difficulty: 2 Medium
Topic: Bayes' Theorem
Learning Objective: 04-05 Use Bayes' Theorem to update prior probabilities to posterior
probabilities.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
13) Bayes' Theorem is always based on two states of nature and three experimental outcomes.
Answer: FALSE
Explanation: Bayes' Theorem can have any number of states of nature and any number of
experimental outcomes.
Difficulty: 2 Medium
Topic: Bayes' Theorem
Learning Objective: 04-05 Use Bayes' Theorem to update prior probabilities to posterior
probabilities.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
207
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written consent of McGraw-Hill Education.
14) A probability model is a mathematic representation of a random phenomenon.
Answer: TRUE
Explanation: With probability, we are dealing with uncertainty of a specific experiment.
Difficulty: 1 Easy
Topic: Probability, Sample Spaces, and Probability Models
Learning Objective: 04-01 Define a probability, a sample space, and a probability model.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
15) There are two types of probability distributions: discrete and binomial.
Answer: FALSE
Explanation: The two types are discrete and continuous. Binomial is a type of discrete
probability distribution.
Difficulty: 2 Medium
Topic: Probability, Sample Spaces, and Probability Models
Learning Objective: 04-01 Define a probability, a sample space, and a probability model.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
16) A random variable is a numerical value that is determined by the outcome of an experiment.
Answer: TRUE
Explanation: This random variable is called a probability distribution.
Difficulty: 1 Easy
Topic: Probability, Sample Spaces, and Probability Models
Learning Objective: 04-01 Define a probability, a sample space, and a probability model.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
208
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written consent of McGraw-Hill Education.
17) Two mutually exclusive events having positive probabilities are ________ dependent.
A) always
B) sometimes
C) never
Answer: A
Explanation: Mutually exclusive events are always dependent on each other because if one
option occurs the other cannot occur.
Difficulty: 2 Medium
Topic: Some Elementary Probability Rules; Conditional Probability and Independence
Learning Objective: 04-03 Use elementary probability rules to compute probabilities.; 04-04
Compute conditional probabilities and assess independence.
Bloom's: Understand
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
18) A ________ is a measure of the chance that an uncertain event will occur.
A) random experiment
B) sample space
C) probability
D) complement
E) population
Answer: C
Explanation: With probability, we are dealing with uncertainty and are applying mathematical
models to predict the chance of something occurring.
Difficulty: 2 Medium
Topic: Probability, Sample Spaces, and Probability Models
Learning Objective: 04-01 Define a probability, a sample space, and a probability model.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
209
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written consent of McGraw-Hill Education.
19) A manager has just received the expense checks for six of her employees. She randomly
distributes the checks to the six employees. What is the probability that exactly five of them will
receive the correct checks (checks with the correct names)?
A) 1
B) 1/2
C) 1/6
D) 0
E) 1/3
Answer: D
Explanation: If five have received the correct check, then it follows that the sixth employee will
receive the correct check. Thus, the probability that exactly five will receive the correct check is
0.
Difficulty: 3 Hard
Topic: Probability, Sample Spaces, and Probability Models
Learning Objective: 04-02 List the outcomes in a sample space and use the list to compute
probabilities.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
20) In which of the following are the two events A and B always independent?
A) A and B are mutually exclusive.
B) The probability of event A is influenced by the probability of event B.
C) The intersection of A and B is zero.
D) P(A|B) = P(B|A).
E) The probability of event A is not influenced by whether event B occurs, or P(A|B) = P(A).
Answer: E
Explanation: The probability of event A is not influenced by whether event B occurs. All of the
other options describe dependent events.
Difficulty: 2 Medium
Topic: Conditional Probability and Independence
Learning Objective: 04-04 Compute conditional probabilities and assess independence.
Bloom's: Understand
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
210
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written consent of McGraw-Hill Education.
21) If two events are independent, we can ________ their probabilities to determine the
intersection probability.
A) divide
B) add
C) multiply
D) subtract
Answer: C
Explanation: This is the multiplication rule for N independent events.
Difficulty: 1 Easy
Topic: Conditional Probability and Independence
Learning Objective: 04-04 Compute conditional probabilities and assess independence.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
22) Events that have no sample space outcomes in common, and therefore cannot occur
simultaneously, are ________.
A) independent
B) mutually exclusive
C) intersections
D) unions
Answer: B
Explanation: This is the classic example of flipping a coin — if you get heads you cannot also
get tails.
Difficulty: 2 Medium
Topic: Some Elementary Probability Rules
Learning Objective: 04-03 Use elementary probability rules to compute probabilities.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
211
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written consent of McGraw-Hill Education.
23) If events A and B are independent, then the probability of simultaneous occurrence of event
A and event B can be found with ________.
A) P(A)·P(B)
B) P(A)·P(B|A)
C) P(B)·P(A|B)
D) All of these choices are correct.
Answer: D
Explanation: All of these notations depict independent events.
Difficulty: 2 Medium
Topic: Conditional Probability and Independence
Learning Objective: 04-04 Compute conditional probabilities and assess independence.
Bloom's: Understand
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
24) The set of all possible outcomes for an experiment is called a(n) ________.
A) sample space
B) event
C) experiment
D) probability
Answer: A
Explanation: We must define the sample space outcomes so that on any single repetition of the
experiment, only one sample space outcome will occur.
Difficulty: 1 Easy
Topic: Probability, Sample Spaces, and Probability Models
Learning Objective: 04-01 Define a probability, a sample space, and a probability model.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
212
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written consent of McGraw-Hill Education.
25) A ________ is the probability that one event will occur given that we know that another
event already has occurred.
A) sample space outcome
B) subjective probability
C) complement of events
D) long-run relative frequency
E) conditional probability
Answer: E
Explanation: The probability of A given B also known as the probability of A given that B has
already occurred.
Difficulty: 2 Medium
Topic: Conditional Probability and Independence
Learning Objective: 04-04 Compute conditional probabilities and assess independence.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
26) The ________ of two events X and Y is another event that consists of the sample space
outcomes belonging to either event X or event Y or both events X and Y.
A) complement
B) union
C) intersection
D) conditional probability
Answer: B
Explanation: The probability that A or B or both will occur.
Difficulty: 2 Medium
Topic: Some Elementary Probability Rules
Learning Objective: 04-03 Use elementary probability rules to compute probabilities.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
213
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written consent of McGraw-Hill Education.
27) If P(A) > 0 and P(B) > 0 and events A and B are independent, then ________.
A) P(A) = P(B)
B) P(A|B) = P(A)
C) P(A∩B) = 0
D) P(A∩B) = P(A) P(B∪A)
Answer: B
Explanation: This is the notation is for independent events. It can also be written as P(B|A) =
P(B).
Difficulty: 2 Medium
Topic: Conditional Probability and Independence
Learning Objective: 04-04 Compute conditional probabilities and assess independence.
Bloom's: Understand
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
28) P(AUB) = P(A) + P(B) − P(A∩B) represents the formula for the ________.
A) conditional probability
B) addition rule
C) addition rule for two mutually exclusive events
D) multiplication rule
Answer: B
Explanation: You need to subtract out the mutually exclusive events because otherwise you
would count them twice.
Difficulty: 2 Medium
Topic: Some Elementary Probability Rules
Learning Objective: 04-03 Use elementary probability rules to compute probabilities.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
29) A(n) ________ is the set of all of the distinct possible outcomes of an experiment.
A) sample space
B) union
C) intersection
D) observation
Answer: A
Explanation: Probabilities must be assigned to the sample space outcomes.
Difficulty: 2 Medium
Topic: Probability, Sample Spaces, and Probability Models
Learning Objective: 04-01 Define a probability, a sample space, and a probability model.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
214
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written consent of McGraw-Hill Education.
30) The ________ of an event is a number that measures the likelihood that an event will occur
when an experiment is carried out.
A) outcome
B) probability
C) intersection
D) observation
Answer: B
Explanation: Probability deals with the concept of measuring uncertainty.
Difficulty: 1 Easy
Topic: Probability, Sample Spaces, and Probability Models
Learning Objective: 04-01 Define a probability, a sample space, and a probability model.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
31) When the probability of one event is influenced by whether or not another event occurs, the
events are said to be ________.
A) independent
B) dependent
C) mutually exclusive
D) experimental
Answer: B
Explanation: This means that if one event occurs, then another event will be more or less likely
to occur because of the first event occurring.
Difficulty: 2 Medium
Topic: Conditional Probability and Independence
Learning Objective: 04-04 Compute conditional probabilities and assess independence.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
215
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written consent of McGraw-Hill Education.
32) A process of observation that has an uncertain outcome is referred to as a(n) ________.
A) probability
B) frequency
C) conditional probability
D) experiment
Answer: D
Explanation: When performing statistical studies, we collect data by performing a controlled
experiment.
Difficulty: 2 Medium
Topic: Probability, Sample Spaces, and Probability Models
Learning Objective: 04-01 Define a probability, a sample space, and a probability model.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
33) When the probability of one event is not influenced by whether or not another event occurs,
the events are said to be ________.
A) independent
B) dependent
C) mutually exclusive
D) experimental
Answer: A
Explanation: This means that events A and B have nothing to do with one another.
Difficulty: 2 Medium
Topic: Conditional Probability and Independence
Learning Objective: 04-04 Compute conditional probabilities and assess independence.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
34) A probability may be interpreted as a long-run ________ frequency.
A) observational
B) relative
C) experimental
D) conditional
Answer: B
Explanation: A relative frequency interpretation of probability is a mathematical idealization.
Difficulty: 2 Medium
Topic: Probability, Sample Spaces, and Probability Models
Learning Objective: 04-01 Define a probability, a sample space, and a probability model.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
216
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written consent of McGraw-Hill Education.
35) If events A and B are independent, then P(A|B) is equal to ________.
A) P(B)
B) P(A∩B)
C) P(A)
D) P(AUB)
Answer: C
Explanation: This is how independent events are denoted.
Difficulty: 2 Medium
Topic: Conditional Probability and Independence
Learning Objective: 04-04 Compute conditional probabilities and assess independence.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
36) The simultaneous occurrence of events A and B is represented by the notation ________.
A) AUB
B) A|B
C) A∩B
D) B|A
Answer: C
Explanation: This is when events A and B occur at the same time.
Difficulty: 1 Easy
Topic: Some Elementary Probability Rules
Learning Objective: 04-03 Use elementary probability rules to compute probabilities.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
217
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written consent of McGraw-Hill Education.
37) A(n) ________ probability is a probability assessment that is based on experience, intuitive
judgment, or expertise.
A) experimental
B) relative frequency
C) objective
D) subjective
Answer: D
Explanation: This is when an individual injects their personal opinion on if an event is judged as
a success or failure.
Difficulty: 2 Medium
Topic: Probability, Sample Spaces, and Probability Models
Learning Objective: 04-01 Define a probability, a sample space, and a probability model.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
38) A(n) ________ is a collection of sample space outcomes.
A) experiment
B) event
C) set
D) probability
Answer: B
Explanation: It is also called experimental outcomes.
Difficulty: 1 Easy
Topic: Probability and Events
Learning Objective: 04-02 List the outcomes in a sample space and use the list to compute
probabilities.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
218
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written consent of McGraw-Hill Education.
39) Probabilities must be assigned to each sample space outcome so that the probabilities of all
the sample space outcomes add up to ________.
A) 1
B) between 0 and 1
C) between −1 and 1
D) 0
Answer: A
Explanation: The probability of an event is always a number between 0 and 1. All of the
probabilities in a sample space add up to 1.
Difficulty: 1 Easy
Topic: Probability, Sample Spaces, and Probability Models
Learning Objective: 04-01 Define a probability, a sample space, and a probability model.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
40) Probabilities must be assigned to sample space outcomes so that the probability assigned to
each sample space outcome must be between ________, inclusive.
A) 0 and 100
B) −100 and 100
C) 0 and 1
D) −1 and 1
Answer: C
Explanation: All of these probabilities in the sample space must add up to 1.
Difficulty: 1 Easy
Topic: Probability, Sample Spaces, and Probability Models
Learning Objective: 04-01 Define a probability, a sample space, and a probability model.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
219
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written consent of McGraw-Hill Education.
41) The ________ of event X consists of all sample space outcomes that do not correspond to the
occurrence of event X.
A) independence
B) complement
C) conditional probability
D) dependence
Answer: B
Explanation: Also known as the probability that X will not occur.
Difficulty: 1 Easy
Topic: Some Elementary Probability Rules
Learning Objective: 04-03 Use elementary probability rules to compute probabilities.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
42) The ________ of two events A and B is the event that consists of the sample space outcomes
belonging to both event A and event B.
A) union
B) intersection
C) complement
D) mutual exclusivity
Answer: B
Explanation: The event that occurs if both A and B occur.
Difficulty: 1 Easy
Topic: Some Elementary Probability Rules
Learning Objective: 04-03 Use elementary probability rules to compute probabilities.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
43) Determine whether these two events are mutually exclusive: consumer with an unlisted
phone number and a consumer who does not drive.
A) mutually exclusive
B) not mutually exclusive
Answer: B
Explanation: In this case, one does not determine the other.
Difficulty: 1 Easy
Topic: Some Elementary Probability Rules
Learning Objective: 04-03 Use elementary probability rules to compute probabilities.
Bloom's: Understand
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
44) Determine whether these two events are mutually exclusive: unmarried person and a person
220
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written consent of McGraw-Hill Education.
with an employed spouse.
A) mutually exclusive
B) not mutually exclusive
Answer: A
Explanation: If you are unmarried you do not have a spouse.
Difficulty: 1 Easy
Topic: Some Elementary Probability Rules
Learning Objective: 04-03 Use elementary probability rules to compute probabilities.
Bloom's: Understand
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
45) Determine whether these two events are mutually exclusive: someone born in the United
States and a U.S. citizen.
A) mutually exclusive
B) not mutually exclusive
Answer: B
Explanation: One event does not affect the other: You do not have to be born in the U.S. to be a
U.S. citizen.
Difficulty: 1 Easy
Topic: Some Elementary Probability Rules
Learning Objective: 04-03 Use elementary probability rules to compute probabilities.
Bloom's: Understand
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
46) Determine whether these two events are mutually exclusive: voter who favors gun control
and an unregistered voter.
A) mutually exclusive
B) not mutually exclusive
Answer: A
Explanation: If you are a voter then you cannot be an unregistered voter.
Difficulty: 1 Easy
Topic: Some Elementary Probability Rules; Conditional Probability and Independence
Learning Objective: 04-03 Use elementary probability rules to compute probabilities.
Bloom's: Understand
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
221
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written consent of McGraw-Hill Education.
47) Determine whether these two events are mutually exclusive: someone with three sisters and
someone with four siblings.
A) mutually exclusive
B) not mutually exclusive
Answer: B
Explanation: If you have four siblings, you could have three sisters or you could have three
brothers.
Difficulty: 1 Easy
Topic: Some Elementary Probability Rules
Learning Objective: 04-03 Use elementary probability rules to compute probabilities.
Bloom's: Understand
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
48) Consider a standard deck of 52 playing cards, a randomly selected card from the deck, and
the following events: R = red, B = black, A = ace, N = nine, D = diamond, and C = club.
Are R and A mutually exclusive?
A) Yes, mutually exclusive.
B) No, not mutually exclusive.
Answer: B
Explanation: In this case, you can have a red ace or a black ace.
Difficulty: 1 Easy
Topic: Some Elementary Probability Rules
Learning Objective: 04-03 Use elementary probability rules to compute probabilities.
Bloom's: Understand
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
49) Consider a standard deck of 52 playing cards, a randomly selected card from the deck, and
the following events: R = red, B = black, A = ace, N = nine, D = diamond, and C = club.
Are R and C mutually exclusive?
A) Yes, mutually exclusive.
B) No, not mutually exclusive.
Answer: A
Explanation: Clubs are only black cards so you cannot have a red club.
Difficulty: 1 Easy
Topic: Some Elementary Probability Rules
Learning Objective: 04-03 Use elementary probability rules to compute probabilities.
Bloom's: Understand
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
222
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written consent of McGraw-Hill Education.
50) Consider a standard deck of 52 playing cards, a randomly selected card from the deck, and
the following events: R = red, B = black, A = ace, N = nine, D = diamond, and C = club.
Are A and N mutually exclusive?
A) Yes, mutually exclusive.
B) No, not mutually exclusive.
Answer: A
Explanation: In this case, you cannot have both an Ace and a nine.
Difficulty: 1 Easy
Topic: Some Elementary Probability Rules
Learning Objective: 04-03 Use elementary probability rules to compute probabilities.
Bloom's: Understand
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
51) Consider a standard deck of 52 playing cards, a randomly selected card from the deck, and
the following events: R = red, B = black, A = ace, N = nine, D = diamond, and C = club.
Are N and C mutually exclusive?
A) Yes, mutually exclusive.
B) No, not mutually exclusive.
Answer: B
Explanation: There is a nine of clubs, but there is also a nine of hearts, spades and diamonds.
Difficulty: 1 Easy
Topic: Some Elementary Probability Rules
Learning Objective: 04-03 Use elementary probability rules to compute probabilities.
Bloom's: Understand
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
52) Consider a standard deck of 52 playing cards, a randomly selected card from the deck, and
the following events: R = red, B = black, A = ace, N = nine, D = diamond, and C = club.
Are D and C mutually exclusive?
A) Yes, mutually exclusive.
B) No, not mutually exclusive.
Answer: A
Explanation: In this case, you cannot have both a diamond and a club at the same time.
Difficulty: 1 Easy
Topic: Some Elementary Probability Rules
Learning Objective: 04-03 Use elementary probability rules to compute probabilities.
Bloom's: Understand
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
223
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written consent of McGraw-Hill Education.
53) The probability model describing an experiment consists of
A) sample space.
B) probabilities of the sample space outcomes.
C) sample space and probabilities of the sample space outcomes.
D) independent events.
E) random variables.
Answer: C
Explanation: They are also called experimental outcomes.
Difficulty: 2 Medium
Topic: Probability, Sample Spaces, and Probability Models
Learning Objective: 04-01 Define a probability, a sample space, and a probability model.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
54) What is the probability of rolling a seven with a pair of fair dice?
A) 6/36
B) 3/36
C) 1/36
D) 8/36
E) 7/36
Answer: A
Explanation: Set up sample spaces: 36 total; 6 have combination adding to 7.
Difficulty: 2 Medium
Topic: Probability and Events
Learning Objective: 04-02 List the outcomes in a sample space and use the list to compute
probabilities.
Bloom's: Understand
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
224
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written consent of McGraw-Hill Education.
55) What is the probability of rolling a value higher than eight with a pair of fair dice?
A) 6/36
B) 18/36
C) 10/36
D) 8/36
E) 12/36
Answer: C
Explanation: Set up sample spaces: 36 total; 10 have combination adding to more than 8.
Difficulty: 2 Medium
Topic: Probability and Events
Learning Objective: 04-02 List the outcomes in a sample space and use the list to compute
probabilities.
Bloom's: Understand
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
56) What is the probability that an even number appears on the toss of a die?
A) 0.5
B) 0.33
C) 0.25
D) 0.67
E) 1.00
Answer: A
Explanation: Set up sample spaces: 6 total; 2, 4, and 6 are even numbers.
Difficulty: 1 Easy
Topic: Probability and Events
Learning Objective: 04-02 List the outcomes in a sample space and use the list to compute
probabilities.
Bloom's: Understand
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
225
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written consent of McGraw-Hill Education.
57) What is the probability that a king appears in drawing a single card from a deck of 52 cards?
A) 4/13
B) 1/13
C) 1/52
D) 1/12
E) 2/13
Answer: B
Explanation: Set up sample spaces: 52; 4 kings in a deck.
Difficulty: 3 Hard
Topic: Probability and Events
Learning Objective: 04-02 List the outcomes in a sample space and use the list to compute
probabilities.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
58) If we consider the toss of four coins as an experiment, how many outcomes does the sample
space consist of?
A) 8
B) 4
C) 16
D) 32
E) 2
Answer: C
Explanation: 24 = 16
Difficulty: 3 Hard
Topic: Counting Rules
Learning Objective: 04-06 Use some elementary counting rules to compute probabilities.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
226
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written consent of McGraw-Hill Education.
59) What is the probability of at least one tail in the toss of three fair coins?
A) 1/8
B) 4/8
C) 5/8
D) 7/8
E) 6/8
Answer: D
Explanation: Set up sample spaces: 8 possibilities; only one has all heads; other 7 have at least
one tail.
Difficulty: 3 Hard
Topic: Probability and Events
Learning Objective: 04-02 List the outcomes in a sample space and use the list to compute
probabilities.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
60) A lot contains 12 items, and 4 are defective. If three items are drawn at random from the lot,
what is the probability they are not defective?
A) 0.3333
B) 0.2545
C) 0.5000
D) 0.2963
E) 0.0370
Answer: B
Explanation:
= .2545
Difficulty: 3 Hard
Topic: Conditional Probability and Independence
Learning Objective: 04-04 Compute conditional probabilities and assess independence.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
227
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written consent of McGraw-Hill Education.
61) A person is dealt 5 cards from a deck of 52 cards. What is the probability they are all clubs?
A) 0.2500
B) 0.0962
C) 0.0769
D) 0.0010
E) 0.0005
Answer: E
Explanation:
= 0.0004951
Difficulty: 3 Hard
Topic: Conditional Probability and Independence
Learning Objective: 04-04 Compute conditional probabilities and assess independence.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
62) A group has 12 men and 4 women. If 3 people are selected at random from the group, what is
the probability that they are all men?
A) 0.4219
B) 0.5143
C) 0.3929
D) 0.0156
E) 0.0045
Answer: C
Explanation:
= .392857
Difficulty: 3 Hard
Topic: Conditional Probability and Independence
Learning Objective: 04-04 Compute conditional probabilities and assess independence.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
228
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written consent of McGraw-Hill Education.
63) Container 1 has 8 items, 3 of which are defective. Container 2 has 5 items, 2 of which are
defective. If one item is drawn from each container, what is the probability that both items are
not defective?
A) 0.3750
B) 0.3846
C) 0.1500
D) 0.6154
E) 0.2000
Answer: A
Explanation:
= .375
Difficulty: 3 Hard
Topic: Conditional Probability and Independence
Learning Objective: 04-04 Compute conditional probabilities and assess independence.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
64) Container 1 has 8 items, 3 of which are defective. Container 2 has 5 items, 2 of which are
defective. If one item is drawn from each container, what is the probability that the item from
Container 1 is defective and the item from Container 2 is not defective?
A) 0.3846
B) 0.2250
C) 0.3750
D) 0.6154
E) 0.1500
Answer: B
Explanation:
= .225
Difficulty: 3 Hard
Topic: Conditional Probability and Independence
Learning Objective: 04-04 Compute conditional probabilities and assess independence.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
229
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written consent of McGraw-Hill Education.
65) Container 1 has 8 items, 3 of which are defective. Container 2 has 5 items, 2 of which are
defective. If one item is drawn from each container, what is the probability that only one of the
items is defective?
A) 0.2250
B) 0.6250
C) 0.2500
D) 0.4750
E) 0.1500
Answer: D
Explanation: Container 1 P(Defective) = 3/8 = .375; Container 2 P(Defective) = 2/5 = .400
P(Both defective) = .375 × .400 = .150; P(Neither defective) = (1 – .375) × (1 – .40) = .375
P(Only one defective) = 1 – (.150 + .375) = .475
Difficulty: 3 Hard
Topic: Conditional Probability and Independence
Learning Objective: 04-04 Compute conditional probabilities and assess independence.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
66) A coin is tossed 6 times. What is the probability that at least one head occurs?
A) 63/64
B) 1/64
C) 1/36
D) 5/6
E) 1/2
Answer: A
Explanation: (1/2)(1/2)(1/2)(1/2)(1/2)(1/2) = P(No Heads) = 1/64
1 – 1/64 = 63/64
Difficulty: 2 Medium
Topic: Conditional Probability and Independence
Learning Objective: 04-04 Compute conditional probabilities and assess independence.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
230
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written consent of McGraw-Hill Education.
67) Given the standard deck of cards, what is the probability of drawing a red card, given that it
is a face card?
A) 0.500
B) 0.115
C) 0.231
D) 0.077
E) 0.308
Answer: A
Explanation:
P(Red | Face) =
=
= .5
Difficulty: 2 Medium
Topic: Conditional Probability and Independence
Learning Objective: 04-04 Compute conditional probabilities and assess independence.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
68) Given a standard deck of cards, what is the probability of drawing a face card, given that it is
a red card?
A) 0.115
B) 0.500
C) 0.231
D) 0.462
E) 0.308
Answer: C
Explanation:
P(Red | Face) =
=
=
Difficulty: 2 Medium
Topic: Conditional Probability and Independence
Learning Objective: 04-04 Compute conditional probabilities and assess independence.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
231
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written consent of McGraw-Hill Education.
69) A machine is made up of 3 components: an upper part, a middle part, and a lower part. The
machine is then assembled. 5 percent of the upper parts are defective, 4 percent of the middle
parts are defective, and 1 percent of the lower parts are defective. What is the probability that a
machine is not defective?
A) 0.1000
B) 0.9029
C) 0.8000
D) 0.0002
E) 0.7209
Answer: B
Explanation: (.95)(.96)(.99) = .9029
Difficulty: 3 Hard
Topic: Conditional Probability and Independence
Learning Objective: 04-04 Compute conditional probabilities and assess independence.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
70) A machine is produced by a sequence of operations. On average, one out of every 1000
machines produced is defective. What is the probability that two machines selected at random
are both nondefective?
A) 0.000999
B) 0.001
C) 0.002
D) 0.998
E) 0.500
Answer: D
Explanation: (.999)(.999) = .998
Difficulty: 2 Medium
Topic: Conditional Probability and Independence
Learning Objective: 04-04 Compute conditional probabilities and assess independence.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
232
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written consent of McGraw-Hill Education.
71) A pair of dice is thrown. What is the probability that one of the faces is a 3, given that the
sum of the two faces is 9?
A) 1/3
B) 1/36
C) 1/6
D) 1/2
E) 1/4
Answer: D
Explanation: Set up sample spaces: 36 total; 4 total to 9; 2 of these have a three on the face.
Given that there are 4 choices and 2 have a three, the probability is ½.
Difficulty: 3 Hard
Topic: Conditional Probability and Independence
Learning Objective: 04-04 Compute conditional probabilities and assess independence.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
72) A card is drawn from a standard deck. What is the probability the card is an ace, given that it
is a club?
A) 1/52
B) 1/13
C) 4/13
D) 1/4
Answer: B
Explanation: Set up sample space: 52 cards; 13 are clubs, one of which is an ace.
Difficulty: 3 Hard
Topic: Conditional Probability and Independence
Learning Objective: 04-04 Compute conditional probabilities and assess independence.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
233
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written consent of McGraw-Hill Education.
73) A card is drawn from a standard deck. Given that a face card is drawn, what is the
probability it will be a king?
A) 1/3
B) 1/13
C) 4/13
D) 1/12
E) 1/4
Answer: A
Explanation: (4 kings)/(12 face cards)
Difficulty: 2 Medium
Topic: Conditional Probability and Independence
Learning Objective: 04-04 Compute conditional probabilities and assess independence.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
74) Independently, a coin is tossed, a card is drawn from a deck, and a die is thrown. What is the
probability of observing a head on the coin, an ace on the card, and a five on the die?
A) 0.0064
B) 0.1000
C) 0.7436
D) 0.0096
E) 0.5000
Answer: A
Explanation: 1/2 × 4/52 × 1/6 = 1/156 = 0.0064
Difficulty: 2 Medium
Topic: Conditional Probability and Independence
Learning Objective: 04-04 Compute conditional probabilities and assess independence.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
234
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written consent of McGraw-Hill Education.
75) A family has two children. What is the probability that both are girls, given that at least one
is a girl?
A) 1/8
B) 1/4
C) 1/2
D) 1/3
E) 1/6
Answer: D
Explanation: Set up sample space: 3 possible for the given statement BG, GB and GG; 2 of
these have at least one girl; 1 has two girls so the probability that GG is 1 out of 3 or 1/3.
Difficulty: 2 Medium
Topic: Conditional Probability and Independence
Learning Objective: 04-04 Compute conditional probabilities and assess independence.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
76) What is the probability of winning four games in a row, if the probability of winning each
game individually is 1/2?
A) 1/4
B) 1/8
C) 1/2
D) 3/16
E) 1/16
Answer: E
Explanation:
=
Difficulty: 2 Medium
Topic: Conditional Probability and Independence
Learning Objective: 04-04 Compute conditional probabilities and assess independence.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
235
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written consent of McGraw-Hill Education.
77) At a college, 70 percent of the students are women, and 50 percent of the students receive a
grade of C. 25 percent of the students are neither female nor C students. Construct a contingency
table.
Answer:
C
Women
Men
0.45
0.05
0.50
0.25
0.25
0.50
0.70
0.30
1.00
Difficulty: 3 Hard
Topic: Some Elementary Probability Rules
Learning Objective: 04-03 Use elementary probability rules to compute probabilities.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
78) At a college, 70 percent of the students are women, and 50 percent of the students receive a
grade of C. 25 percent of the students are neither female nor C students. Use this contingency
table.
C
Women
Men
0.45
0.05
0.50
0.25
0.25
0.50
0.70
0.30
1.00
What is the probability that a student is female and a C student?
A) .45
B) .50
C) .70
D) .25
E) .05
Answer: A
Explanation: Read off contingency table = P(F ∩ C) = .45
Difficulty: 3 Hard
Topic: Some Elementary Probability Rules
Learning Objective: 04-03 Use elementary probability rules to compute probabilities.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
236
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written consent of McGraw-Hill Education.
79) At a college, 70 percent of the students are women, and 50 percent of the students receive a
grade of C. 25 percent of the students are neither female nor C students. Use this contingency
table.
C
Women
Men
0.45
0.05
0.50
0.25
0.25
0.50
0.70
0.30
1.00
What is the probability that a student is male and not a C student?
A) .45
B) .50
C) .70
D) .25
E) .05
Answer: D
Explanation: Read off contingency table: P(M ∩ not C) = .25
Difficulty: 3 Hard
Topic: Some Elementary Probability Rules
Learning Objective: 04-03 Use elementary probability rules to compute probabilities.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
237
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written consent of McGraw-Hill Education.
80) At a college, 70 percent of the students are women, and 50 percent of the students receive a
grade of C. 25 percent of the students are neither female nor C students. Use this contingency
table.
C
Women
Men
0.45
0.05
0.50
0.25
0.25
0.50
0.70
0.30
1.00
If a student is male, what is the probability he is a C student?
A) 0.05
B) 0.10
C) 0.30
D) 0.17
E) 0.50
Answer: D
Explanation:
P(C | Male) =
= .1667
Difficulty: 3 Hard
Topic: Conditional Probability and Independence
Learning Objective: 04-04 Compute conditional probabilities and assess independence.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
238
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written consent of McGraw-Hill Education.
81) At a college, 70 percent of the students are women, and 50 percent of the students receive a
grade of C. 25 percent of the students are neither female nor C students. Use this contingency
table.
C
Women
Men
0.45
0.05
0.50
0.25
0.25
0.50
0.70
0.30
1.00
If a student has received a grade of C, what is the probability that the student is male?
A) 0.05
B) 0.10
C) 0.30
D) 0.17
E) 0.50
Answer: B
Explanation:
P(Male | C) =
= .10
Difficulty: 3 Hard
Topic: Conditional Probability and Independence
Learning Objective: 04-04 Compute conditional probabilities and assess independence.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
239
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written consent of McGraw-Hill Education.
82) At a college, 70 percent of the students are women and 50 percent of the students receive a
grade of C. 25 percent of the students are neither female nor C students. Use this contingency
table.
C
Women
Men
0.45
0.05
0.50
0.25
0.25
0.50
0.70
0.30
1.00
If a student has received a grade of C, what is the probability that the student is female?
A) 0.45
B) 0.90
C) 0.70
D) 0.64
E) 0.50
Answer: B
Explanation:
P(female | C) =
= .90
Difficulty: 3 Hard
Topic: Conditional Probability and Independence
Learning Objective: 04-04 Compute conditional probabilities and assess independence.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
240
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written consent of McGraw-Hill Education.
83) Two percent of the customers of a store buy cigars. Half of the customers who buy cigars
buy beer. 25 percent who buy beer buy cigars. Determine the probability that a customer buys
beer.
A) 0.25
B) 0.01
C) 0.04
D) 0.50
E) 0.005
Answer: C
Explanation:
Cigars
P(Beer) =
Beer
.01
.03
.04
.01
.95
.96
=
.02
.98
1.0
= .04
Difficulty: 3 Hard
Topic: Conditional Probability and Independence
Learning Objective: 04-04 Compute conditional probabilities and assess independence.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
241
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written consent of McGraw-Hill Education.
84) Two percent of the customers of a store buy cigars. Half of the customers who buy cigars
buy beer. 25 percent who buy beer buy cigars. Determine the probability that a customer neither
buys beer nor buys cigars.
A) 0.98
B) 0.95
C) 0.75
D) 0.96
E) 0.50
Answer: B
Explanation:
Cigars
Beer
.01
.03
.04
.01
.95
.96
.02
.98
1.0
Difficulty: 2 Medium
Topic: Conditional Probability and Independence
Learning Objective: 04-04 Compute conditional probabilities and assess independence.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
85) An urn contains five white, three red, and four black balls. Three are drawn at random and
not placed back into the urn. What is the probability that no ball is red?
A) 0.7500
B) 0.0156
C) 0.2917
D) 0.4219
E) 0.3818
Answer: E
Explanation:
= .3818
Difficulty: 3 Hard
Topic: Conditional Probability and Independence
Learning Objective: 04-04 Compute conditional probabilities and assess independence.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
242
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written consent of McGraw-Hill Education.
86) The probability of event A occurring given that event B has already occurred is 0.61. The
probability of both events occurring is 0.5. What is the probability of event B occurring?
A) 0.305
B) 0.195
C) 0.390
D) 0.820
E) 0.500
Answer: D
Explanation: P(B) = P(A ∩ B) / P(A | B) = .5/.61 = 0.81967
Difficulty: 2 Medium
Topic: Conditional Probability and Independence
Learning Objective: 04-04 Compute conditional probabilities and assess independence.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
87) What is the probability that any two people chosen at random were born on the same day of
the week?
A) 1/7
B) 1/49
C) 2/7
D) 2/49
Answer: A
Explanation: Set up sample space: 72 = 49; same day: 7 sample space outcomes.
Difficulty: 3 Hard
Topic: Conditional Probability and Independence
Learning Objective: 04-04 Compute conditional probabilities and assess independence.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
243
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written consent of McGraw-Hill Education.
88) A letter is drawn from the alphabet of 26 letters. What is the probability that the letter drawn
is a vowel?
A) 5/26
B) 1/26
C) 4/26
D) 21/26
Answer: A
Explanation: AEIOU; 5 vowels out of 26 letters.
Difficulty: 1 Easy
Topic: Probability and Events
Learning Objective: 04-02 List the outcomes in a sample space and use the list to compute
probabilities.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
89) If A and B are independent events, P(A) = .2, and P(B) = .7, determine P(A ∪ B).
A) 0.90
B) 0.14
C) 0.76
D) 0.50
E) 0.24
Answer: C
Explanation:
P(A ∪ B) = P(A) + P(B) - P(A ∩ B)
P(A ∪ B) = (.7) + (.2) - (.7)(.2) = .76
Difficulty: 1 Easy
Topic: Some Elementary Probability Rules
Learning Objective: 04-03 Use elementary probability rules to compute probabilities.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
244
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written consent of McGraw-Hill Education.
90) If events A and B are mutually exclusive, calculate P(A|B).
A) Cannot be determined.
B) 0
C) 1
D) 0.50
Answer: B
Explanation: Mutually exclusive events have intersection = 0. Therefore, the conditional
probability is also 0.
Difficulty: 3 Hard
Topic: Some Elementary Probability Rules
Learning Objective: 04-03 Use elementary probability rules to compute probabilities.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
91) What is the probability of rolling a six with a fair die five times in a row?
A) 1/6
B) 1/46,656
C) 1/7,776
D) 5/7,776
Answer: C
Explanation: (1/6)5 = 1/7,776
Difficulty: 3 Hard
Topic: Conditional Probability and Independence
Learning Objective: 04-04 Compute conditional probabilities and assess independence.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
245
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written consent of McGraw-Hill Education.
92) If a product is made using five individual components, and P(product meets specifications) =
P(E) = .98, what is the probability of an individual component meeting specifications, assuming
that this probability is the same for all five components?
A) 0.98
B) 0.996
C) 0.004
D) 0.02
E) 0.904
Answer: B
Explanation:
= .996
Difficulty: 3 Hard
Topic: Conditional Probability and Independence
Learning Objective: 04-04 Compute conditional probabilities and assess independence.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
93) If P(A|B) = .2 and P(B) = .8, determine the intersection of events A and B.
A) 0.20
B) 1.0
C) 0.25
D) 0.16
E) 0.60
Answer: D
Explanation: (.2)(.8) = .16
Difficulty: 2 Medium
Topic: Conditional Probability and Independence
Learning Objective: 04-04 Compute conditional probabilities and assess independence.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
246
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written consent of McGraw-Hill Education.
94) If P(A ∩ B ) = .3 and P(A | B) = .9, find P(B).
A) 0.6
B) 0.3
C) 0.5
D) 0.27
E) 0.33
Answer: E
Explanation: P(B) =
= .333
Difficulty: 2 Medium
Topic: Conditional Probability and Independence
Learning Objective: 04-04 Compute conditional probabilities and assess independence.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
95) Employees of a local university have been classified according to gender and job type.
Job
Faculty (FA)
Salaried Staff (SS)
Hourly Staff (HS)
Gender
Male (M)
Female (F)
110
10
30
50
60
40
If an employee is selected at random, what is the probability that the employee is male?
A) .667
B) .367
C) .333
D) .500
E) .917
Answer: A
Explanation: P(M) =
= .667
Difficulty: 2 Medium
Topic: Probability and Events
Learning Objective: 04-02 List the outcomes in a sample space and use the list to compute
probabilities.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
247
Copyright 2019 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior
written consent of McGraw-Hill Education.
96) Employees of a local university have been classified according to gender and job type.
Job
Faculty (FA)
Salaried Staff (SS)
Hourly Staff (HS)
Gender
Male (M)
Female (F)
110
10
30
50
60
40
If an employee is selected at random, what is the probability that the employee is male and
salaried staff?
A) .15
B) .10
C) .38
D) .50
E) .85
Answer: B
Explanation: P(M and SS) =
= 0.10
Difficulty: 2 Medium
Topic: Some Elementary Probability Rules
Learning Objective: 04-03 Use elementary probability rules to compute probabilities.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
248
Copyright 2019 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior
written consent of McGraw-Hill Education.
97) Employees of a local university have been classified according to gender and job type.
Gender
Male (M)
Female (F)
110
10
30
50
60
40
Job
Faculty (FA)
Salaried Staff (SS)
Hourly Staff (HS)
If an employee is selected at random, what is the probability that the employee is female, given
that the employee is a salaried member of the staff?
A) .167
B) .500
C) .625
D) 267
E) .375
Answer: C
Explanation: P(F | SS) =
=
= 0.625
Difficulty: 2 Medium
Topic: Conditional Probability and Independence
Learning Objective: 04-04 Compute conditional probabilities and assess independence.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
249
Copyright 2019 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior
written consent of McGraw-Hill Education.
98) Employees of a local university have been classified according to gender and job type.
Job
Faculty (FA)
Salaried Staff (SS)
Hourly Staff (HS)
Gender
Male (M)
Female (F)
110
10
30
50
60
40
If an employee is selected at random, what is the probability that the employee is female or
works as a member of the faculty?
A) 0.73
B) 0.08
C) 0.33
D) 0.70
E) 0.05
Answer: D
Explanation: P(F ∪ FA) =
+
-
= 0.70
Difficulty: 2 Medium
Topic: Some Elementary Probability Rules
Learning Objective: 04-03 Use elementary probability rules to compute probabilities.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
250
Copyright 2019 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior
written consent of McGraw-Hill Education.
99) Employees of a local university have been classified according to gender and job type.
Job
Faculty (FA)
Salaried Staff (SS)
Hourly Staff (HS)
Gender
Male (M)
Female (F)
110
10
30
50
60
40
If an employee is selected at random, what is the probability that the employee is female or
works as an hourly staff member?
A) 0.133
B) 0.533
C) 0.667
D) 0.400
E) 0.333
Answer: B
Explanation: P(F ∪ HA) =
+
-
= 0.533
Difficulty: 2 Medium
Topic: Some Elementary Probability Rules
Learning Objective: 04-03 Use elementary probability rules to compute probabilities.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
251
Copyright 2019 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior
written consent of McGraw-Hill Education.
100) Employees of a local university have been classified according to gender and job type.
Gender
Male (M)
Female (F)
110
10
30
50
60
40
Job
Faculty (FA)
Salaried Staff (SS)
Hourly Staff (HS)
If an employee is selected at random, what is the probability that the employee is a member of
the hourly staff, given that the employee is female?
A) 0.400
B) 0.133
C) 0.160
D) 0.053
E) 0.533
Answer: A
Explanation: P(HS | F) =
=
= 0.400
Difficulty: 2 Medium
Topic: Conditional Probability and Independence
Learning Objective: 04-04 Compute conditional probabilities and assess independence.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
252
Copyright 2019 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior
written consent of McGraw-Hill Education.
101) Employees of a local university have been classified according to gender and job type.
Job
Faculty (FA)
Salaried Staff (SS)
Hourly Staff (HS)
Gender
Male (M)
Female (F)
110
10
30
50
60
40
If an employee is selected at random, what is the probability that the employee is a member of
the faculty?
A) 0.333
B) 0.600
C) 0.550
D) 0.400
E) 0.917
Answer: D
Explanation: P(FA) =
= .40
Difficulty: 2 Medium
Topic: Probability and Events
Learning Objective: 04-02 List the outcomes in a sample space and use the list to compute
probabilities.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
253
Copyright 2019 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior
written consent of McGraw-Hill Education.
102) Employees of a local university have been classified according to gender and job type.
Gender
Male (M)
Female (F)
110
10
30
50
60
40
Job
Faculty (FA)
Salaried Staff (SS)
Hourly Staff (HS)
Are gender and type of job mutually exclusive?
A) Yes
B) No
Answer: B
Explanation: No, gender and job type are not mutually exclusive.
P(M) =
= .667
P(FA) =
P(M ∩ FA) =
= 0.40
≠0
Difficulty: 2 Medium
Topic: Some Elementary Probability Rules
Learning Objective: 04-03 Use elementary probability rules to compute probabilities.
Bloom's: Analyze
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
254
Copyright 2019 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior
written consent of McGraw-Hill Education.
103) Employees of a local university have been classified according to gender and job type.
Gender
Male (M)
Female (F)
110
10
30
50
60
40
Job
Faculty (FA)
Salaried Staff (SS)
Hourly Staff (HS)
Are gender and type of job statistically independent?
A) Yes
B) No
Answer: B
Explanation: No, gender is not independent of type of job.
Select a category of gender (male) and a category of job status (faculty), if the two are
independent of each other, then:
P(M) = P(M | FA)
Since P(M) =
and P(M | FA) =
= 0.667
= 0.9167
0.667 ≠ 0.9167
Difficulty: 2 Medium
Topic: Conditional Probability and Independence
Learning Objective: 04-04 Compute conditional probabilities and assess independence.
Bloom's: Analyze
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
255
Copyright 2019 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior
written consent of McGraw-Hill Education.
104) Four employees who work as drive-through attendants at a local fast-food restaurant are
being evaluated. As part of a quality improvement initiative and employee evaluation, these
workers were observed over three days. One of the statistics collected was the proportion of time
the employee forgot to include a napkin in the bag. Also recorded was the proportion of all
dinners packed by each employee. Related information is given in the table.
Worker
Joe
Jan
Cheryl
Clay
Dinner Packed
25%
20%
20%
35%
Dinner Packed With
No Napkin
6%
2%
10%
4%
What is the probability that Cheryl packed a given dinner and forgot to include a napkin?
A) 0.20
B) 0.10
C) 0.45
D) 0.02
E) 0.30
Answer: D
Explanation: P(Cheryl ∩ Forgot napkin) = (.20)(.10) = 0.02
Difficulty: 2 Medium
Topic: Some Elementary Probability Rules; Conditional Probability and Independence
Learning Objective: 04-03 Use elementary probability rules to compute probabilities.; 04-04
Compute conditional probabilities and assess independence.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
256
Copyright 2019 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior
written consent of McGraw-Hill Education.
105) Four employees who work as drive-through attendants at a local fast-food restaurant are
being evaluated. As part of a quality improvement initiative and employee evaluation, these
workers were observed over three days. One of the statistics collected was the proportion of time
the employee forgot to include a napkin in the bag. Also recorded was the proportion of all
dinners packed by each employee. Related information is given in the table.
Worker
Joe
Jan
Cheryl
Clay
Dinner Packed
25%
20%
20%
35%
Dinner Packed With
No Napkin
6%
2%
10%
4%
What is the probability that there is not a napkin included for a given order?
A) 0.22
B) 0.24
C) 0.053
D) 0.015
E) 0.04
Answer: C
Explanation: P(No Napkin) = (.25)(.06) + (.20)(.02) + (0.20)(.10) + (.35)(.04) = .053
Difficulty: 2 Medium
Topic: Some Elementary Probability Rules; Conditional Probability and Independence
Learning Objective: 04-03 Use elementary probability rules to compute probabilities.; 04-04
Compute conditional probabilities and assess independence.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
257
Copyright 2019 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior
written consent of McGraw-Hill Education.
106) Four employees who work as drive-through attendants at a local fast-food restaurant are
being evaluated. As part of a quality improvement initiative and employee evaluation, these
workers were observed over three days. One of the statistics collected was the proportion of time
the employee forgot to include a napkin in the bag. Also recorded was the proportion of all
dinners packed by each employee. Related information is given in the table.
Worker
Joe
Jan
Cheryl
Clay
Dinner Packed
25%
20%
20%
35%
Dinner Packed With
No Napkin
6%
2%
10%
4%
You just purchased a dinner and found that there is no napkin in your bag. What is the
probability that Cheryl prepared your order?
A) 0.377
B) 0.091
C) 0.083
D) 0.500
E) 0.020
Answer: A
Explanation:
P(Cheryl | No napkin) =
=
= .37774
Difficulty: 3 Hard
Topic: Some Elementary Probability Rules; Conditional Probability and Independence
Learning Objective: 04-03 Use elementary probability rules to compute probabilities.; 04-04
Compute conditional probabilities and assess independence.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
258
Copyright 2019 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior
written consent of McGraw-Hill Education.
107) Four employees who work as drive-through attendants at a local fast-food restaurant are
being evaluated. As part of a quality improvement initiative and employee evaluation, these
workers were observed over three days. One of the statistics collected was the proportion of time
the employee forgot to include a napkin in the bag. Also recorded was the proportion of all
dinners packed by each employee. Related information is given in the table.
Worker
Joe
Jan
Cheryl
Clay
Dinner Packed
25%
20%
20%
35%
Dinner Packed With
No Napkin
6%
2%
10%
4%
You just purchased a dinner and found that there is no napkin in your bag. What is the
probability that Jan prepared your order?
A) 0.200
B) 0.004
C) 0.018
D) 0.075
E) 0.100
Answer: D
Explanation:
P(Jan | No napkin) =
=
= .0755
Difficulty: 3 Hard
Topic: Some Elementary Probability Rules; Conditional Probability and Independence
Learning Objective: 04-03 Use elementary probability rules to compute probabilities.; 04-04
Compute conditional probabilities and assess independence.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
259
Copyright 2019 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior
written consent of McGraw-Hill Education.
108) Joe is considering pursuing an MBA degree. He has applied to two different universities.
The acceptance rate for applicants with similar qualifications is 25 percent for University A and
40 percent for University B.
What is the probability that Joe will be accepted at both universities?
A) 0.10
B) 0.25
C) 0.65
D) 0.625
E) 0.40
Answer: A
Explanation: (.25)(.40) = 0.10
Difficulty: 3 Hard
Topic: Conditional Probability and Independence
Learning Objective: 04-04 Compute conditional probabilities and assess independence.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
109) Joe is considering pursuing an MBA degree. He has applied to two different universities.
The acceptance rate for applicants with similar qualifications is 25 percent for University A and
40 percent for University B.
What is the probability that Joe will be accepted at University A and rejected at University B?
A) 0.10
B) 0.85
C) 0.15
D) 0.25
E) 0.65
Answer: C
Explanation: (.25)(.60) = 0.15
Difficulty: 2 Medium
Topic: Conditional Probability and Independence
Learning Objective: 04-04 Compute conditional probabilities and assess independence.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
260
Copyright 2019 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior
written consent of McGraw-Hill Education.
110) Joe is considering pursuing an MBA degree. He has applied to two different universities.
The acceptance rate for applicants with similar qualifications is 25 percent for University A and
40 percent for University B.
What is the probability that Joe will not be accepted at either university?
A) 0.75
B) 0.45
C) 0.90
D) 0.65
E) 0.60
Answer: B
Explanation: (.75)(.60) = 0.45
Difficulty: 2 Medium
Topic: Conditional Probability and Independence
Learning Objective: 04-04 Compute conditional probabilities and assess independence.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
111) Joe is considering pursuing an MBA degree. He has applied to two different universities.
The acceptance rate for applicants with similar qualifications is 25 percent for University A and
40 percent for University B.
What is the probability that Joe will be accepted by at least one of the two universities?
A) 0.25
B) 0.55
C) 0.10
D) 0.35
E) 0.40
Answer: B
Explanation: 1 − (.75)(.60) = 0.55
Difficulty: 2 Medium
Topic: Conditional Probability and Independence
Learning Objective: 04-04 Compute conditional probabilities and assess independence.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
261
Copyright 2019 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior
written consent of McGraw-Hill Education.
112) Joe is considering pursuing an MBA degree. He has applied to two different universities.
The acceptance rate for applicants with similar qualifications is 25 percent for University A and
40 percent for University B.
What is the probability that Joe will be accepted at one, and only one, university?
A) 0.50
B) 0.10
C) 0.15
D) 0.30
E) 0.45
Answer: E
Explanation: (.25)(.60) + (.75)(.40) = 0.45
Difficulty: 3 Hard
Topic: Conditional Probability and Independence
Learning Objective: 04-04 Compute conditional probabilities and assess independence.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
113) Joe is considering pursuing an MBA degree. He has applied to two different universities.
The acceptance rate for applicants with similar qualifications is 25 percent for University A and
40 percent for University B. Of the applicants with similar qualities, only 10 percent are accepted
into both University A and University B.
Is the acceptance decision at University A independent of the acceptance decision at University
B?
A) Yes
B) No
Answer: A
Explanation: Yes, the two decisions are statistically independent. If the MBA acceptance
decisions are independent at the two universities, then
P(Accepted at A) = P(Accepted at A given Rejected at B).
P(Accepted at A) = .25 = P(Accept at A | Reject at B)
=
=
= .25
Difficulty: 3 Hard
Topic: Conditional Probability and Independence
Learning Objective: 04-04 Compute conditional probabilities and assess independence.
Bloom's: Analyze
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
262
Copyright 2019 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior
written consent of McGraw-Hill Education.
114) A report on high school graduation stated that 85 percent of high school students graduate.
Suppose 3 high school students are randomly selected from different schools.
What is the probability that all graduate?
A) 0.85
B) 0.947
C) 0.614
D) 0.283
E) 0.003
Answer: C
Explanation: (.85)(.85)(.85) = 0.614
Difficulty: 2 Medium
Topic: Conditional Probability and Independence
Learning Objective: 04-04 Compute conditional probabilities and assess independence.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
115) A report on high school graduation stated that 85 percent of high school students graduate.
Suppose 3 high school students are randomly selected from different schools.
What is the probability that exactly one of the three graduates?
A) 0.019
B) 0.003
C) 0.614
D) 0.057
E) 0.850
Answer: D
Explanation: (.85)(.15)(.15) + (.15)(.85)(.15) + (.15)(.15)(.85) = .057375
Difficulty: 3 Hard
Topic: Conditional Probability and Independence
Learning Objective: 04-04 Compute conditional probabilities and assess independence.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
263
Copyright 2019 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior
written consent of McGraw-Hill Education.
116) A report on high school graduation stated that 85 percent of high school students graduate.
Suppose 3 high school students are randomly selected from different schools.
What is the probability that none will graduate?
A) 0.019
B) 0.003
C) 0.614
D) 0.057
E) 0.150
Answer: B
Explanation: (.15)(.15)(.15) = .003375
Difficulty: 2 Medium
Topic: Conditional Probability and Independence
Learning Objective: 04-04 Compute conditional probabilities and assess independence.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
117) It is very common for a television series to draw a large audience for special events or for
cliff-hanging story lines. Suppose that on one of these occasions, the special show drew viewers
from 38.2 percent of all US TV households. Suppose that three TV households are randomly
selected.
What is the probability that all three households viewed this special show?
A) 0.382
B) 0.127
C) 0.146
D) 0.726
E) 0.056
Answer: E
Explanation: (.382)(.382)(.382) = .05574
Difficulty: 1 Easy
Topic: Conditional Probability and Independence
Learning Objective: 04-04 Compute conditional probabilities and assess independence.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
264
Copyright 2019 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior
written consent of McGraw-Hill Education.
118) It is very common for a television series to draw a large audience for special events or for
cliff-hanging story lines. Suppose that on one of these occasions, the special show drew viewers
from 38.2 percent of all US TV households. Suppose that three TV households are randomly
selected.
What is the probability that none of the three households viewed this special show?
A) 0.236
B) 0.056
C) 0.618
D) 0.382
E) 0.127
Answer: A
Explanation: (.618)(.618)(.618) = .236
Difficulty: 1 Easy
Topic: Conditional Probability and Independence
Learning Objective: 04-04 Compute conditional probabilities and assess independence.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
119) It is very common for a television series to draw a large audience for special events or for
cliff-hanging story lines. Suppose that on one of these occasions, the special show drew viewers
from 38.2 percent of all US TV households. Suppose that three TV households are randomly
selected.
What is the probability that exactly one of the three households viewed the special show?
A) 0.146
B) 0.084
C) 0.438
D) 0.382
E) 0.056
Answer: C
Explanation: (.382)(.618)(.618) + (.618)(.382)(.618) + (.618)(.618)(.382) = .4376
Difficulty: 3 Hard
Topic: Conditional Probability and Independence
Learning Objective: 04-04 Compute conditional probabilities and assess independence.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
265
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written consent of McGraw-Hill Education.
120) A survey is made in a neighborhood of 80 voters. 65 are Democrats and 15 are
Republicans. Of the Democrats, 35 are women, while 5 of the Republicans are women. If one
subject from the group is randomly selected, find the probability the individual is either a woman
or a Democrat.
A) .538
B) .813
C) .500
D) .438
E) .875
Answer: E
Explanation:
P(W ∪ D) = P(W) + P(D) - P(W ∩ D)
= (40/80) + (65/80) - (35/80) = .877
Difficulty: 2 Medium
Topic: Some Elementary Probability Rules
Learning Objective: 04-03 Use elementary probability rules to compute probabilities.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
121) A survey is made in a neighborhood of 80 voters. 65 are Democrats and 15 are
Republicans. Of the Democrats, 35 are women, while 5 of the Republicans are women. If one
subject from the group is randomly selected, find the probability the individual is a male
Republican.
A) .125
B) .500
C) .333
D) .667
E) .188
Answer: A
Explanation: (10/80) = .125
Difficulty: 2 Medium
Topic: Probability and Events
Learning Objective: 04-02 List the outcomes in a sample space and use the list to compute
probabilities.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
266
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written consent of McGraw-Hill Education.
122) A survey is made in a neighborhood of 80 voters. 65 are Democrats and 15 are
Republicans. Of the Democrats, 35 are women, while 5 of the Republicans are women. If one
subject from the group is randomly selected, find the probability the individual is a Democrat or
a Republican.
A) 0.50
B) 1.00
C) 0.813
D) 0.188
E) 0.152
Answer: B
Explanation: All voters in the survey were either D or R. Therefore, the probability is 1.
Difficulty: 1 Easy
Topic: Some Elementary Probability Rules
Learning Objective: 04-03 Use elementary probability rules to compute probabilities.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
123) New car owners were asked to evaluate their experiences in buying a new car during the
past 12 months. In the survey, the owners indicated they were most satisfied with their
experiences at the following three dealers (in no particular order): Subaru, Honda, and Buick.
When ranking the dealers, how many outcomes are possible?
A) 6
B) 9
C) 8
D) 10
E) 12
Answer: A
Explanation: HSB, BHS, SHB, HBS, BSH, SBH
Difficulty: 1 Easy
Topic: Probability and Events
Learning Objective: 04-02 List the outcomes in a sample space and use the list to compute
probabilities.
Bloom's: Understand
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
267
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written consent of McGraw-Hill Education.
124) New car owners were asked to evaluate their experiences in buying a new car during the
past 12 months. In the survey, the owners indicated they were most satisfied with their
experiences at the following three dealers (in no particular order): Subaru, Honda, and Buick.
Assuming that each set of rankings is equally likely, what is the probability that owners ranked
Subaru first?
A) 1/3
B) 1/6
C) 1/2
D) 5/6
E) 6/6
Answer: A
Explanation: Sample spaces: HSB, BHS, SHB, HBS, BSH, SBH; 2/6, or 1/3
Difficulty: 1 Easy
Topic: Probability and Events
Learning Objective: 04-02 List the outcomes in a sample space and use the list to compute
probabilities.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
125) New car owners were asked to evaluate their experiences in buying a new car during the
past 12 months. In the survey, the owners indicated they were most satisfied with their
experiences at the following three dealers (in no particular order): Subaru, Honda, and Buick.
Assuming that each set of rankings is equally likely, what is the probability that owners ranked
Subaru third?
A) 1/3
B) 1/6
C) 1/2
D) 5/6
E) 6/6
Answer: A
Explanation: Sample spaces: HSB, BHS, SHB, HBS, BSH, SBH; 2/6, or 1/3
Difficulty: 1 Easy
Topic: Probability and Events
Learning Objective: 04-02 List the outcomes in a sample space and use the list to compute
probabilities.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
268
Copyright 2019 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior
written consent of McGraw-Hill Education.
126) New car owners were asked to evaluate their experiences in buying a new car during the
past 12 months. In the survey, the owners indicated they were most satisfied with their
experiences at the following three dealers (in no particular order): Subaru, Honda, and Buick.
Assuming that each set of rankings is equally likely, what is the probability that owners ranked
Subaru first and Honda second?
A) 1/3
B) 1/6
C) 1/2
D) 5/6
E) 6/6
Answer: B
Explanation: HSB, BHS, SHB, HBS, BSH, SBH; 1/6
Difficulty: 1 Easy
Topic: Probability and Events
Learning Objective: 04-02 List the outcomes in a sample space and use the list to compute
probabilities.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
127) In a study of chain saw injuries, 57 percent involved arms or hands. If three different chain
saw injury cases are randomly selected, find the probability that they all involved arms or hands.
A) 0.570
B) 0.190
C) 0.185
D) 0.829
E) 0.325
Answer: C
Explanation: (.57)(.57)(.57) = .185
Difficulty: 1 Easy
Topic: Conditional Probability and Independence
Learning Objective: 04-04 Compute conditional probabilities and assess independence.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
269
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written consent of McGraw-Hill Education.
128) In a local survey, 100 citizens indicated their opinions on a revision to a local land-use plan.
Of the 62 persons giving favorable responses, 40 were males. Of the 38 giving unfavorable
responses, 15 were males. If one citizen is randomly selected, find the probability that person is
female or has an unfavorable opinion.
A) 0.83
B) 0.17
C) 0.51
D) 0.60
E) 0.61
Answer: D
Explanation: P(F ∪ N) = P(F) + P(N) - P(F ∩ N) = .45 + .38 - .23 = .60
M
F
Y
40
22
62
N
15
23
38
65
45
100
Difficulty: 2 Medium
Topic: Some Elementary Probability Rules
Learning Objective: 04-03 Use elementary probability rules to compute probabilities.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
129) In a local survey, 100 citizens indicated their opinions on a revision to a local land-use plan.
Of the 62 persons giving favorable responses, 40 were males. Of the 38 giving unfavorable
responses, 15 were males. If one citizen is randomly selected, find the probability that person is
male and has a favorable opinion.
A) 0.40
B) 0.65
C) 0.62
D) 0.55
E) 0.25
Answer: A
Explanation: 40/100
Difficulty: 1 Easy
Topic: Some Elementary Probability Rules
Learning Objective: 04-03 Use elementary probability rules to compute probabilities.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
270
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written consent of McGraw-Hill Education.
130) In a local survey, 100 citizens indicated their opinions on a revision to a local land-use plan.
Of the 62 persons giving favorable responses, 40 were males. Of the 38 giving unfavorable
responses, 15 were males. If one citizen is randomly selected, find the probability that person has
a favorable opinion or has an unfavorable opinion
A) 0.00
B) 1.00
C) 0.62
D) 0.24
Answer: B
Explanation: There are only the two types of responses, favorable and unfavorable. Thus, the
probability = 1.0.
Difficulty: 1 Easy
Topic: Some Elementary Probability Rules
Learning Objective: 04-03 Use elementary probability rules to compute probabilities.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
131) A batch of 50 parts contains 6 defects. If two parts are drawn randomly, one at a time, and
tested, what is the probability that both parts are defective?
A) 0.014
B) 0.012
C) 0.120
D) 0.102
E) 0.222
Answer: B
Explanation: (6/50)(5/49) = .012
Difficulty: 2 Medium
Topic: Conditional Probability and Independence
Learning Objective: 04-04 Compute conditional probabilities and assess independence.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
271
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written consent of McGraw-Hill Education.
132) Suppose that you believe that the probability you will get a grade of B or better in
Introduction to Finance is .6 and the probability that you will get a grade of B or better in
Introduction to Accounting is .5. If these events are independent, what is the probability that you
will receive a grade of B or better in both courses?
A) 0.300
B) 0.833
C) 0.600
D) 0.500
E) 0.800
Answer: A
Explanation: (.6)(.5) = .30
Difficulty: 1 Easy
Topic: Conditional Probability and Independence
Learning Objective: 04-04 Compute conditional probabilities and assess independence.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
272
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written consent of McGraw-Hill Education.
133) In a major midwestern university, 55 percent of all undergraduates are female, 25 percent of
all undergraduates belong to a Greek organization (fraternity or sorority), and 40 percent of all
males belong to a Greek organization. What percentage of the undergraduates are female and in a
Greek organization?
A) 55%
B) 25%
C) 60%
D) 7%
E) 15%
Answer: D
Explanation: To complete the contingency table and answer the question on the
intersection of female and Greek, since the initial information includes a conditional
statement, you need to calculate the intersection of female and Greek: If P(Greek │ Male)
= 40%. And 40% of .45 = .18. Then, Female & Greek = .25 − .18 = .07, or 7%
Greek
Non-Greek
Female
.07
.48
.55
Male
.18
.27
.45
.25
.75
Difficulty: 3 Hard
Topic: Some Elementary Probability Rules; Conditional Probability and Independence
Learning Objective: 04-03 Use elementary probability rules to compute probabilities.; 04-04
Compute conditional probabilities and assess independence.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
273
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written consent of McGraw-Hill Education.
134) In a major midwestern university, 55 percent of all undergraduates are female, 25 percent of
all undergraduates belong to a Greek organization (fraternity or sorority), and 40 percent of all
males belong to a Greek organization. What is the probability that one randomly selected
undergraduate will be either a female or belong to a Greek organization?
A) .73
B) .55
C) .80
D) .07
E) .87
Answer: A
Explanation: To complete the contingency table and answer the question on the
intersection of female or Greek, since the initial information includes a conditional
statement, you need to calculate the intersection of male and Greek:
If P(Greek │ Male) = 40%. And 40% of .45 = .18. Then, Female & Greek = .25 − .18 =
.07, or 7%. P(Female) = 55%. P(Greek) = 25%.
P(G ∪ F) = .55 + .25 − .07 = .73
Greek
Non-Greek
Fem
ale
.07
.48
.55
Mal
e
.18
.27
.45
.25
.75
Difficulty: 3 Hard
Topic: Some Elementary Probability Rules; Conditional Probability and Independence
Learning Objective: 04-03 Use elementary probability rules to compute probabilities.; 04-04
Compute conditional probabilities and assess independence.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
274
Copyright 2019 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior
written consent of McGraw-Hill Education.
135) In a major midwestern university, 55 percent of all undergraduates are female, 25 percent of
all undergraduates belong to a Greek organization (fraternity or sorority), and 40 percent of all
males belong to a Greek organization. What is the probability that an undergraduate is in a Greek
organization, given that the undergraduate is a female?
A) .07
B) .55
C) .127
D) .039
E) 138
Answer: C
Explanation: To complete the contingency table and answer the question on the
intersection of female or Greek, since the initial information includes a conditional
statement, you need to calculate the intersection of male and Greek: If P(Greek │ Male)
= 40%. And 40% of .45 = .18. Then, Female & Greek = .25 − .18 = .07, or 7%.
P(Female) = 55%.
P(G|F) = .07/.55 = .127
Greek
Non-Greek
Fem
ale
.07
.48
.55
Mal
e
.18
.27
.45
.25
.75
Difficulty: 3 Hard
Topic: Conditional Probability and Independence
Learning Objective: 04-04 Compute conditional probabilities and assess independence.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
275
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written consent of McGraw-Hill Education.
136) In a major midwestern university, 55 percent of all undergraduates are female, 25 percent of
all undergraduates belong to a Greek organization (fraternity or sorority), and 40 percent of all
males belong to a Greek organization. Are the events "female " and "belongs to a Greek
organization" independent?
A) Yes, independent.
B) No, not independent.
Answer: B
Explanation: P(G|F) = .07/.55 = .127 ≠ P(G)
Difficulty: 3 Hard
Topic: Conditional Probability and Independence
Learning Objective: 04-04 Compute conditional probabilities and assess independence.
Bloom's: Analyze
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
137) An ad agency is developing a campaign to promote a business opening in a new mall
development. To develop an appropriate mailing list, they decide to purchase lists of credit card
holders from MasterCard and American Express. Combining the lists, they find the following: 40
percent of the people on the list have only a MasterCard and 10 percent have only an American
Express card. Another 20 percent hold both MasterCard and American Express. Finally, 30
percent of those on the list have neither card. Suppose a person on the list is known to have a
MasterCard. What is the probability that person also has an American Express card?
A) .20
B) .33
C) .18
D) .70
E) .90
Answer: B
Explanation: P(AE|MC) = .20/.60 = .33
American Express
No American Express
MasterCard
.20
.40
.60
No MasterCard
.10
.30
.40
.30
.70
1.00
Difficulty: 2 Medium
Topic: Conditional Probability and Independence
Learning Objective: 04-04 Compute conditional probabilities and assess independence.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
276
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written consent of McGraw-Hill Education.
138) Suppose that A1, A2, and B are events where A1 and A2 are mutually exclusive events and
P(A1) = .7, P(A2) = .3, P(B│A1) = .2, P(B│A2) = .4. Find P(B).
A) 0.60
B) 0.26
C) 0.21
D) 0.14
E) 0.28
Answer: B
Explanation: P(B) = P(A1) × P(B│A1) + P(A2) × P(B│A2) = (.7)(.2) + (.3)(.4) = .26
Difficulty: 3 Hard
Topic: Bayes' Theorem
Learning Objective: 04-05 Use Bayes' Theorem to update prior probabilities to posterior
probabilities.
Bloom's: Understand
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
139) Suppose that A1, A2, and B are events where A1 and A2 are mutually exclusive events and
P(A1) = .7, P(A2) = .3, P(B│A1) = .2, P(B│A2) = .4. Find P(A1│B).
A) 0.12
B) 0.26
C) 0.21
D) 0.54
E) 0.28
Answer: D
Explanation: P(A1│B) = P(A1∩B)/P(B) = .14/.26 = .54
Difficulty: 3 Hard
Topic: Bayes' Theorem
Learning Objective: 04-05 Use Bayes' Theorem to update prior probabilities to posterior
probabilities.
Bloom's: Understand
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
277
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written consent of McGraw-Hill Education.
140) Suppose that A1, A2, and B are events where A1 and A2 are mutually exclusive events and
P(A1) = .7, P(A2) = .3, P(B│A1) = .2, P(B│A2) = .4. Find P(A2│B).
A) 0.12
B) 0.26
C) 0.21
D) 0.14
E) 0.46
Answer: E
Explanation: P(A2│B) = P(A2∩B)/P(B) = .12/.26 = .46
Difficulty: 3 Hard
Topic: Bayes' Theorem
Learning Objective: 04-05 Use Bayes' Theorem to update prior probabilities to posterior
probabilities.
Bloom's: Understand
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
141) Suppose that 60 percent of a company's computer chips are manufactured in Factory A,
while 40 percent are produced in Factory B [P(A) = .60 for a randomly selected chip]. The defect
rates for the two factories are 35 percent for Factory A and 25 percent for Factory B. Suppose we
now know that the randomly selected chip is defective. Find the probability that the defective
chip comes from Factory A.
Answer: .677
P(A│Defective) = P(A ∩ Defective)/[P(A) × P(Defective│A) + P(B) × P(Defective│B)]
= (.6 × .35)/[(.6 × .35) + (.4 × .25)] = .677
Difficulty: 3 Hard
Topic: Bayes' Theorem
Learning Objective: 04-05 Use Bayes' Theorem to update prior probabilities to posterior
probabilities.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
278
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written consent of McGraw-Hill Education.
142) A television program director has 14 shows available for Monday night but can choose only
5 shows. How many different possible combinations are there?
Answer: 2002
14!/5!9!
Difficulty: 2 Medium
Topic: Counting Rules
Learning Objective: 04-06 Use some elementary counting rules to compute probabilities.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
143) An auditing firm has developed a set of criteria for determining whether a particular
account (and its balance) is in error. Historically, they know that of balances that were in error,
75 percent were regarded as unusual. Assume Company A shows a history of only 10 percent of
the account balances being in error and it also shows that 25 percent of the account balances
were unusual. If in an audit, a particular account balance appears unusual, what is the probability
that it is in error for Company A?
Answer: .30
P(Error) = .10
P(Unusual) = .25
P(Unusual│Error) = .75
P(Error│Unusual) for Company A = P(Unusual│Error) × P(Error)/P(Unusual)
= (.75 × .10)/.25 = .30
Difficulty: 3 Hard
Topic: Bayes' Theorem
Learning Objective: 04-05 Use Bayes' Theorem to update prior probabilities to posterior
probabilities.
Bloom's: Understand
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
279
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written consent of McGraw-Hill Education.
144) An auditing firm has developed a set of criteria for determining whether a particular
account (and its balance) is in error. Historically, they know that of balances that were in error,
75 percent were regarded as unusual. Assume Company A shows a history of only 10 percent of
the account balances being in error and it also shows that 25 percent of the account balances
were unusual. What are the states of nature and the experimental outcomes?
Answer: States of Nature are "Error in account balance" and "No error in account balance;"
Experimental Outcomes are "Account balance appears unusual" and "Account balance does not
appear unusual."
Difficulty: 3 Hard
Topic: Bayes' Theorem
Learning Objective: 04-05 Use Bayes' Theorem to update prior probabilities to posterior
probabilities.
Bloom's: Understand
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
145) A worldwide personal products manufacturer is working on a new hair care product. In the
past, 85 percent of new hair care products introduced by this company have become successful
(15 percent have failed). Obviously, the marketing research department plays a large role in the
introduction of any new product. Historically, 85 percent of the successful products have a
favorable rating from marketing research studies and 20 percent of the unsuccessful products
have favorable ratings. For the new hair care product, the marketing unit has issued a favorable
rating. What is the probability that the new product will be successful?
Answer: .96
P(Success) = P(S) = .85
P(Unsuccessful) = P(U) = .15
Event F = Favorable
Event NF = Not favorable
P(F│S) = .85
P(F│U) = .20
P(S│F) = (.85 × .85)/[(.85 × .85) + (.20 × .15)] = .96
Difficulty: 3 Hard
Topic: Bayes' Theorem
Learning Objective: 04-05 Use Bayes' Theorem to update prior probabilities to posterior
probabilities.
Bloom's: Understand
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
280
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written consent of McGraw-Hill Education.
146) Suppose the probability that an individual has a particular medical condition is .10. Tests of
an individual's DNA can determine whether they have this medical condition but with only an 85
percent accuracy rate (that is, if the condition is present, the probability that the DNA test will
give a positive finding is .85). If the medical condition is not present, the probability of the DNA
test saying the medical condition exists is 0.03. What is the probability that the medical condition
is present if the DNA test comes back positive?
Answer: .76
P(MC exists) = P(MC) = .10
P(MC doesn't exist) = P(NMC) = .90
Event D = DNA test positive
Event ND = DNA test not positive
P(D│MC) = .85
P(D│NMC) = .03
P(MC│D) = (.85 × .10)/[(.85 × .10) + (.03 × .9)] = .759
Difficulty: 3 Hard
Topic: Bayes' Theorem
Learning Objective: 04-05 Use Bayes' Theorem to update prior probabilities to posterior
probabilities.
Bloom's: Understand
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
281
Copyright 2019 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior
written consent of McGraw-Hill Education.
147) Three companies produce all the potato chips used by vending machines in public areas in a
midwestern state. Company A accounts for 70 percent of the chips, Company B 19 percent, and
Company C 11 percent. The probability of the vending company getting an unfilled bag is 2
percent for Company A, 2 percent for Company B, and 4 percent for Company C. Suppose an
unfilled bag is found. What is the probability that it came from Company A?
Answer: .63
P(A) = .70
P(B) = .19
P(C) = .11
P(U│A) = .02
P(U│B) = .02
P(U│C) = .04
P(U) = P(A∩U) + P(B∩U) + P(C∩U) = .014 + .0038 + .0044 = .0222
P(A│U) = P(A∩U)/P(U) = .014/.0222 = .63
Difficulty: 3 Hard
Topic: Bayes' Theorem
Learning Objective: 04-05 Use Bayes' Theorem to update prior probabilities to posterior
probabilities.
Bloom's: Understand
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
282
Copyright 2019 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior
written consent of McGraw-Hill Education.
148) Three companies produce all the potato chips used by vending machines in public areas in a
midwestern state. Company A accounts for 70 percent of the chips, Company B 19 percent, and
Company C 11 percent. The probability of the vending company getting an unfilled bag is 2
percent for Company A, 2 percent for Company B, and 4 percent for Company C. Suppose an
unfilled bag is found. What is the probability that it came from Company B?
Answer: .17
P(A) = .70
P(B) = .19
P(C) = .11
P(U│A) = .02
P(U│B) = .02
P(U│C) = .04
P(U) = P(A ∩ U) + P(B ∩ U) + P(C ∩ U) = .014 + .0038 + .0044 = .0222
P(B│U) = P(B ∩ U)/P(U) = .0038/.0222 = .17
Difficulty: 3 Hard
Topic: Bayes' Theorem
Learning Objective: 04-05 Use Bayes' Theorem to update prior probabilities to posterior
probabilities.
Bloom's: Understand
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
283
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written consent of McGraw-Hill Education.
149) Three companies produce all the potato chips used by vending machines in public areas in a
midwestern state. Company A accounts for 70 percent of the chips, Company B 19 percent, and
Company C 11 percent. The probability of the vending company getting an unfilled bag is 2
percent for Company A, 2 percent for Company B, and 4 percent for Company C. Suppose an
unfilled bag is found. What is the probability that it came from Company C?
Answer: .20
P(A) = .70
P(B) = .19
P(C) = .11
P(U│A) = .02
P(U│B) = .02
P(U│C) = .04
P(U) = P(A ∩ U) + P(B ∩ U) + P(C ∩ U) = .014 + .0038 + .0044 = .0222
P(C│U) = P(C ∩ U)/P(U) = .0044/.0222 = .1982
Difficulty: 3 Hard
Topic: Bayes' Theorem
Learning Objective: 04-05 Use Bayes' Theorem to update prior probabilities to posterior
probabilities.
Bloom's: Understand
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
284
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written consent of McGraw-Hill Education.
150) Every current applicant for a position in the marketing department of Company A is given a
10-question test on interpretation of findings from statistical analyses. Individuals are rated on
three levels based on their scores: Excellent (9-10 correct), Average (5-8 correct), and Poor
(fewer than 5 correct). Historically, the probability of an individual scoring Excellent = .38,
Average = .52, and Poor = .10. Also, the company knows that 90 percent of applicants who score
Excellent are offered a position, 75 percent of applicants who score Average are offered a
position, and 35 percent of the applicants who score Poor are offered a position. What is the
probability that an individual who is offered a position has an Excellent score?
Answer: .446
P(E) = .38
P(A) = .52
P(P) = .10
P(O│E) = .90
P(O│A) = .75
P(O│P) = .35
P(O) = P(E ∩ O) + P(A ∩ O) + P(P ∩ O) = .342 + .39 + .035 = .767
P(E│O) = P(E ∩ O)/P(O) = .342/.767 = .446
Difficulty: 3 Hard
Topic: Bayes' Theorem
Learning Objective: 04-05 Use Bayes' Theorem to update prior probabilities to posterior
probabilities.
Bloom's: Understand
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
285
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written consent of McGraw-Hill Education.
151) Every current applicant for a position in the marketing department of Company A is given a
10-question test on interpretation of findings from statistical analyses. Individuals are rated on
three levels based on their scores: Excellent (9-10 correct), Average (5-8 correct), and Poor
(fewer than 5 correct). Historically, the probability of an individual scoring Excellent = .38,
Average = .52, and Poor = .10. Also, the company knows that 90 percent of applicants who score
Excellent are offered a position, 75 percent of applicants who score Average are offered a
position, and 35 percent of the applicants who score Poor are offered a position. What is the
probability that an individual who is offered a position has an Average score?
Answer: .508
P(E) = .38
P(A) = .52
P(P) = .10
P(O│E) = .90
P(O│A) = .75
P(O│P) = .35
P(O) = P(E∩O) + P(A ∩ O) + P(P ∩ O) = .342 + .39 + .035 = .767
P(A│O) = P(A ∩ O)/P(O) = .39/.767 = .508
Difficulty: 3 Hard
Topic: Bayes' Theorem
Learning Objective: 04-05 Use Bayes' Theorem to update prior probabilities to posterior
probabilities.
Bloom's: Understand
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
286
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written consent of McGraw-Hill Education.
152) Every current applicant for a position in the marketing department of Company A is given a
10-question test on interpretation of findings from statistical analyses. Individuals are rated on
three levels based on their scores: Excellent (9-10 correct), Average (5-8 correct), and Poor
(fewer than 5 correct). Historically, the probability of an individual scoring Excellent = .38,
Average = .52, and Poor = .10. Also, the company knows that 90 percent of applicants who score
Excellent are offered a position, 75 percent of applicants who score Average are offered a
position, and 35 percent of the applicants who score Poor are offered a position. What is the
probability that an individual who is offered a position has a Poor score?
Answer: .046
P(E) = .38
P(A) = .52
P(P) = .10
P(O│E) = .90
P(O│A) = .75
P(O│P) = .35
P(O) = P(E ∩ O) + P(A ∩ O) + P(P ∩ O) = .342 + .39 + .035 = .767
P(P│O) = P(P ∩ O)/P(O) = .035/.767 = .046
Difficulty: 3 Hard
Topic: Bayes' Theorem
Learning Objective: 04-05 Use Bayes' Theorem to update prior probabilities to posterior
probabilities.
Bloom's: Understand
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
287
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written consent of McGraw-Hill Education.
1) The binomial experiment consists of n independent, identical trials, each of which results in
either success or failure and is such that the probability of success on any trial is the same.
Answer: TRUE
Explanation: This is the definition of the binomial model. All of these characteristics need to be
met.
Difficulty: 1 Easy
Topic: The Binomial Distribution
Learning Objective: 06-03 Use the binomial distribution to compute probabilities.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
2) A Poisson random variable is a continuous variable that can be used to describe the number of
occurrences of an event over a specified interval of time or space.
Answer: FALSE
Explanation: Poisson random variables are not continuous, they are discrete.
Difficulty: 1 Easy
Topic: The Poisson Distribution
Learning Objective: 06-04 Use the Poisson distribution to compute probabilities.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
3) A discrete random variable may assume a countable sequence or list.
Answer: TRUE
Explanation: It may assume a finite number of possible values or a countable sequence i.e. 1, 2,
3, 4, etc.
Difficulty: 1 Easy
Topic: Two Types of Random Variables
Learning Objective: 06-01 Explain the difference between a discrete random variable and a
continuous random variable.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
288
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written consent of McGraw-Hill Education.
4) The variable Home Ownership can take on one of two values: 1 if the person living in the
home owns the home and 0 if the person living in the home does not own the home. This is an
example of a discrete random variable.
Answer: TRUE
Explanation: Because this variable has a finite number of possible values (either 0 or 1), it is a
discrete random variable.
Difficulty: 1 Easy
Topic: Two Types of Random Variables
Learning Objective: 06-01 Explain the difference between a discrete random variable and a
continuous random variable.
Bloom's: Understand
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
5) If the number of surface nonconformities on a specific size of a metal piece is the discrete
random variable in question, then the appropriate probability distribution that can describe the
probability of a specific size metal sheet containing 3 nonconformities is most likely given by the
binomial distribution.
Answer: FALSE
Explanation: This example is a description of a hypergeometric distribution.
Difficulty: 2 Medium
Topic: The Binomial Distribution
Learning Objective: 06-03 Use the binomial distribution to compute probabilities.
Bloom's: Understand
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
6) The mean of the binomial random variable is np(1 − p).
Answer: FALSE
Explanation: The mean of the binomial random variable is np.
Difficulty: 1 Easy
Topic: The Binomial Distribution
Learning Objective: 06-03 Use the binomial distribution to compute probabilities.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
289
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written consent of McGraw-Hill Education.
7) In a binomial experiment, the results of one trial are dependent on the results of other trials.
Answer: FALSE
Explanation: One assumption of the binomial distribution is independence of trials.
Difficulty: 1 Easy
Topic: The Binomial Distribution
Learning Objective: 06-03 Use the binomial distribution to compute probabilities.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
8) In a binomial distribution, the random variable x is continuous.
Answer: FALSE
Explanation: The binomial distribution defines the random variable x as discrete.
Difficulty: 1 Easy
Topic: The Binomial Distribution
Learning Objective: 06-03 Use the binomial distribution to compute probabilities.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
9) The internal auditor for your company believes that 10 percent of their invoices contain errors.
To check this theory, 20 invoices are randomly selected and 5 are found to have errors.
Based on the above information, the claim of the auditor will be rejected.
Answer: TRUE
Explanation: Reject claim because P < .05.
Difficulty: 3 Hard
Topic: The Binomial Distribution
Learning Objective: 06-03 Use the binomial distribution to compute probabilities.
Bloom's: Analyze
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
10) The mean and the variance of a Poisson random variable are equal.
Answer: TRUE
Explanation: This is part of the definition of the Poisson random variable.
Difficulty: 1 Easy
Topic: The Poisson Distribution
Learning Objective: 06-04 Use the Poisson distribution to compute probabilities.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
290
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written consent of McGraw-Hill Education.
11) Depending on the mean of the Poisson distribution, the distribution can either be very
skewed to the right or can be quite symmetrical.
Answer: TRUE
Explanation: The Poisson distribution is not skewed to the left.
Difficulty: 1 Easy
Topic: The Poisson Distribution
Learning Objective: 06-04 Use the Poisson distribution to compute probabilities.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
12) For a discrete probability distribution, the value of p(x) for each value of x falls between −1
and 1.
Answer: FALSE
Explanation: Probability values, p(x), can only fall between 0 and 1.
Difficulty: 1 Easy
Topic: Discrete Probability Distributions
Learning Objective: 06-02 Find a discrete probability distribution and compute its mean and
standard deviation.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
13) The expected value of the discrete random variable x is the population mean.
Answer: TRUE
Explanation: In order to calculate the expected value, we multiply each value of x by its
probability p(x) and then sum the resulting products over all possible values of x.
Difficulty: 1 Easy
Topic: Discrete Probability Distributions
Learning Objective: 06-02 Find a discrete probability distribution and compute its mean and
standard deviation.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
291
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written consent of McGraw-Hill Education.
14) The standard deviation of a discrete random variable measures the spread of the population
of all possible values of x.
Answer: TRUE
Explanation: The standard deviation can tell you how clustered or spread out the population of
all possible values of x is.
Difficulty: 1 Easy
Topic: Discrete Probability Distributions
Learning Objective: 06-02 Find a discrete probability distribution and compute its mean and
standard deviation.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
15) The time (in seconds) it takes for an athlete to run 50 meters is an example of a continuous
random variable.
Answer: TRUE
Explanation: The time it could take the athlete to run 50 meters could be any value between 0
and infinity.
Difficulty: 2 Medium
Topic: Two Types of Random Variables
Learning Objective: 06-01 Explain the difference between a discrete random variable and a
continuous random variable.
Bloom's: Understand
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
16) The hypergeometric probability distribution can be approximated by the Poisson distribution.
Answer: FALSE
Explanation: The hypergeometric distribution is approximated by a binomial distribution.
Difficulty: 1 Easy
Topic: The Hypergeometric Distribution
Learning Objective: 06-05 Use the hypergeometric distribution to compute probabilities.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
292
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written consent of McGraw-Hill Education.
17) If the population size is at least 20 times larger than the sample size, a hypergeometric
distribution can be approximated by the binomial distribution.
Answer: TRUE
Explanation: The population size needs to be much larger and the definition says 20 times larger
than the sample size taken.
Difficulty: 1 Easy
Topic: The Hypergeometric Distribution
Learning Objective: 06-05 Use the hypergeometric distribution to compute probabilities.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
18) In a hypergeometric probability distribution of a population of N items, r refers to the
number of successes and N − r refers to the number of failures.
Answer: TRUE
Explanation: N refers to the number of items and r are the items that are successes. Therefore,
by definition, N − r would be total − successes = failures.
Difficulty: 1 Easy
Topic: The Hypergeometric Distribution
Learning Objective: 06-05 Use the hypergeometric distribution to compute probabilities.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
19) With two random variables x and y, a positive covariance says that as x increases, y tends to
increase in a linear fashion.
Answer: TRUE
Explanation: This is shown on an x, y scatter plot; as one increases the other does as well.
Difficulty: 1 Easy
Topic: Joint Distributions and the Covariance
Learning Objective: 06-06 Compute and understand the covariance between two random
variables.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
293
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written consent of McGraw-Hill Education.
20) A correlation coefficient is a unitless measure of the linear relationship between two random
variables.
Answer: TRUE
Explanation: It can be positive or negative.
Difficulty: 1 Easy
Topic: Joint Distributions and the Covariance
Learning Objective: 06-06 Compute and understand the covariance between two random
variables.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
21) The property of expected values says if a and b are constants, and if x and y are random
variables, then μ (ax +by) = aμx + bμy + 2ab.
Answer: FALSE
Explanation: The property of expected values does not include the value 2ab.
Difficulty: 1 Easy
Topic: Joint Distributions and the Covariance
Learning Objective: 06-06 Compute and understand the covariance between two random
variables.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
22) The random variable x has a hypergeometric distribution and the population contains 12
items. If you wanted to find the number of defects in a random sample of 3 selected items when
the population contains 5 defects, identify the N, n, and r.
A) N = 3, n = 12, r = 5
B) N = 5, n = 12, r = 2
C) N = 12, n = 5, r = 3
D) N = 12, n = 3, r = 5
Answer: D
Explanation: In the hypergeometric distribution, N is the number of items in the population, r
the number of successes, and n a random sample of the population N.
Difficulty: 2 Medium
Topic: The Hypergeometric Distribution
Learning Objective: 06-05 Use the hypergeometric distribution to compute probabilities.
Bloom's: Understand
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
294
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written consent of McGraw-Hill Education.
23) A hypergeometric random variable x has a distribution that is approximated by a binomial
distribution when
A) the number of successes is larger than the number of failures in the population.
B) a sample is selected from the population without replacement.
C) the population is much larger (about 20 times larger) than the sample size.
D) the sample size is half the size of the original population.
Answer: C
Explanation: This is by definition — much larger is 20 times larger.
Difficulty: 1 Easy
Topic: The Hypergeometric Distribution
Learning Objective: 06-05 Use the hypergeometric distribution to compute probabilities.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
24) In the context of the hypergeometric distribution, r is
A) the sample size.
B) the number of items in the population that are successes.
C) the number of items that are sampled without replacement.
D) the number of items in the sample that are successes.
Answer: B
Explanation: N is the number of items and r is the number of those items that were successes.
Difficulty: 1 Easy
Topic: The Hypergeometric Distribution
Learning Objective: 06-05 Use the hypergeometric distribution to compute probabilities.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
25) Which of the following is not a discrete random variable?
A) the number of times a light changes red in a 10-minute cycle
B) the number of minutes required to run 1 mile
C) the number of defects in a sample selected from a population of 100 products
D) the number of criminals found in a five-mile radius of a neighborhood
Answer: B
Explanation: It could take someone infinite number of minutes to finish the 1 mile.
Difficulty: 2 Medium
Topic: Two Types of Random Variables
Learning Objective: 06-01 Explain the difference between a discrete random variable and a
continuous random variable.
Bloom's: Understand
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
295
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written consent of McGraw-Hill Education.
26) A random variable
A) is the result of a measurement.
B) can only be discrete.
C) assigns one and only one numeric value to each experimental outcome.
D) is a binomial, Poisson, or hypergeometric variable.
Answer: C
Explanation: A random variable is countable.
Difficulty: 1 Easy
Topic: Two Types of Random Variables
Learning Objective: 06-01 Explain the difference between a discrete random variable and a
continuous random variable.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
27) A discrete probability distribution is expressed as a table, graph, or ________ that gives the
probability associated with each possible value that the random variable can assume.
A) binomial
B) formula
C) Poisson
D) hypergeometric
Answer: B
Explanation: This distribution, no matter how it is displayed, will sum to 1.
Difficulty: 1 Easy
Topic: Discrete Probability Distributions
Learning Objective: 06-02 Find a discrete probability distribution and compute its mean and
standard deviation.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
296
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written consent of McGraw-Hill Education.
28) Using the following probability distribution table of the random variable x, what is the
probability of x = 3?
X
0
1
2
3
P(X)
5/15
4/15
1/15
A) 3/15
B) 5/15
C) 1/15
D) 2/15
Answer: B
Explanation: All values of P(X) need to sum to 1, so 5/15 + 4/15 + 1/15 = 10/15 means P(X = 3)
= 5/15.
Difficulty: 2 Medium
Topic: Discrete Probability Distributions
Learning Objective: 06-02 Find a discrete probability distribution and compute its mean and
standard deviation.
Bloom's: Understand
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
29) The probability distribution of a random variable that is defined to be the number of
successes obtained in a random sample selected without replacement from a finite population of
N elements that contains r successes and N − r failures is
A) Poisson.
B) binomial.
C) hypergeometric.
D) discrete.
Answer: C
Explanation: This is the definition of a hypergeometric distribution. The population must be 20
times larger than the sample size.
Difficulty: 1 Easy
Topic: The Hypergeometric Distribution
Learning Objective: 06-05 Use the hypergeometric distribution to compute probabilities.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
297
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written consent of McGraw-Hill Education.
30) The mean of a hypergeometric random variable is defined as
A) n(r/N).
B) N(r/n).
C) npq.
D) np.
Answer: A
Explanation: This is where N is the population size, n is the sample size and r is the number of
successes.
Difficulty: 1 Easy
Topic: The Hypergeometric Distribution
Learning Objective: 06-05 Use the hypergeometric distribution to compute probabilities.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
31) If p = .1 and n = 5, then the corresponding binomial distribution is ________.
A) right skewed
B) left skewed
C) symmetric
D) bimodal
Answer: A
Explanation: Most of the values for this binomial distribution are on the left-hand side of the
graph.
Difficulty: 3 Hard
Topic: The Binomial Distribution
Learning Objective: 06-03 Use the binomial distribution to compute probabilities.
Bloom's: Analyze
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
32) If p = .5 and n = 4, then the corresponding binomial distribution is ________.
A) right skewed
B) left skewed
C) symmetric
D) bimodal
Answer: C
Explanation: It is similar to a bell curve.
Difficulty: 3 Hard
Topic: The Binomial Distribution
Learning Objective: 06-03 Use the binomial distribution to compute probabilities.
Bloom's: Analyze
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
298
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written consent of McGraw-Hill Education.
33) The requirement that the probability of success remains constant from trial to trial is a
property of the ________ distribution.
A) binomial
B) uniform
C) normal
D) Poisson
Answer: A
Explanation: Each trial is not affected by previous successes or failures.
Difficulty: 1 Easy
Topic: The Binomial Distribution
Learning Objective: 06-03 Use the binomial distribution to compute probabilities.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
34) If the number of surface nonconformities on a specific size of metal piece is the discrete
random variable in question, then the appropriate probability distribution that can describe the
probability of a specific size metal sheet containing 3 defects is given most likely by ________
distribution(s).
A) the binomial
B) the Poisson
C) the hypergeometric
D) both the binomial and Poisson
Answer: C
Explanation: In this case we can assume that the probability of a success is essentially constant
from selection to selection.
Difficulty: 2 Medium
Topic: The Hypergeometric Distribution
Learning Objective: 06-05 Use the hypergeometric distribution to compute probabilities.
Bloom's: Understand
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
299
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written consent of McGraw-Hill Education.
35) Which of the following distributions can be used to solve the following problem?
The average number of cars arriving at a drive-through fast-food restaurant is 3 cars in 10
minutes. What is the probability that exactly four cars will arrive in a 5-minute interval?
A) binomial
B) Poisson
C) both binomial and Poisson
D) neither binomial nor Poisson
Answer: B
Explanation: A Poisson would be the best choice because it looks at the number of times an
event occurs an interval of time or space.
Difficulty: 3 Hard
Topic: The Poisson Distribution
Learning Objective: 06-04 Use the Poisson distribution to compute probabilities.
Bloom's: Analyze
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
36) The mean of the binomial distribution is equal to
A) p.
B) np.
C) px(1 − p)n−x.
D) (n)(p)(1 − p).
E)
(1 − p)
Answer: B
Explanation: Where n is the number of trials and p is the probability of success on each trial.
Difficulty: 1 Easy
Topic: The Binomial Distribution
Learning Objective: 06-03 Use the binomial distribution to compute probabilities.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
300
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written consent of McGraw-Hill Education.
37) The number of ways to arrange x successes among n trials is equal to
A)
.
B)
.
C) .
D)
.
Answer: A
Explanation: N is the number of trials in an experiment and x is the number of successes in that
experiment.
Difficulty: 1 Easy
Topic: The Binomial Distribution
Learning Objective: 06-03 Use the binomial distribution to compute probabilities.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
38) Which of the following is a valid probability value for a discrete random variable?
A) .2
B) 1.01
C) −.7
D) All of the choices are correct.
Answer: A
Explanation: The probability of a discrete random variable can only be between 0 and +1.
Difficulty: 1 Easy
Topic: Discrete Probability Distributions
Learning Objective: 06-02 Find a discrete probability distribution and compute its mean and
standard deviation.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
301
Copyright 2019 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior
written consent of McGraw-Hill Education.
39) A total of 50 raffle tickets are sold for a contest to win a car. If you purchase one ticket, what
are your odds against winning?
A) 49 to 1
B) 50 to 1
C) .05
D) .01
Answer: A
Explanation: Probability of losing = 1 − probability of winning = 1 − 1/50 = 49/50.
Difficulty: 3 Hard
Topic: Discrete Probability Distributions
Learning Objective: 06-02 Find a discrete probability distribution and compute its mean and
standard deviation.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
40) Which one of the following statements is not an assumption of the binomial distribution?
A) Sampling is with replacement.
B) The experiment consists of an identical trial.
C) The probability of success remains constant from trial to trial.
D) Trials are independent of each other.
E) Each trial results in one of two mutually exclusive outcomes.
Answer: A
Explanation: All trials are independent and you do not replace once you have a success or
failure.
Difficulty: 1 Easy
Topic: The Binomial Distribution
Learning Objective: 06-03 Use the binomial distribution to compute probabilities.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
302
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written consent of McGraw-Hill Education.
41) The binomial distribution is characterized by situations that are analogous to
A) drawing balls from an urn.
B) coin tossing.
C) counting defects on an item.
D) measuring the length of an item.
Answer: B
Explanation: Binomial distributions assume a constant probability of success.
Difficulty: 2 Medium
Topic: The Binomial Distribution
Learning Objective: 06-03 Use the binomial distribution to compute probabilities.
Bloom's: Understand
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
42) Two characteristics, or assumptions, of the Poisson distribution are that
A) the probability of success remains constant from trial to trial, and the random variable of
interest is continuous.
B) the event occurring in any interval is independent of the event occurring in any other
nonoverlapping interval, and the random variable of interest is continuous.
C) the event occurring in any interval is independent of the event occurring in any other
nonoverlapping interval, and the random variable of interest is discrete.
D) the event occurring in any interval is dependent on the event occurring in any other
nonoverlapping interval, and the random variable of interest is continuous.
Answer: C
Explanation: The random variable must be discrete, i.e., countable, and independent; a success
in a previous trial does not dictate a success in a current trial.
Difficulty: 1 Easy
Topic: The Poisson Distribution
Learning Objective: 06-04 Use the Poisson distribution to compute probabilities.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
303
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written consent of McGraw-Hill Education.
43) The variable Employment Status, which can take either the value 1 for Employed or 0 for
Unemployed, is an example of a ________ random variable.
A) Poisson
B) discrete
C) hypergeometric
D) continuous
Answer: B
Explanation: The variable is countable and is either one or the other; it cannot be both employed
and unemployed at the same time.
Difficulty: 1 Easy
Topic: Two Types of Random Variables
Learning Objective: 06-01 Explain the difference between a discrete random variable and a
continuous random variable.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
44) If x is a binomial random variable, then the standard deviation of x is given by
A) np.
B) (npq)2.
C)
.
D) npq.
Answer: C
Explanation: Where n is the number of trials, p is the number of successes and q is the number
of failures.
Difficulty: 1 Easy
Topic: The Binomial Distribution
Learning Objective: 06-03 Use the binomial distribution to compute probabilities.
Bloom's: Remember
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
304
Copyright 2019 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior
written consent of McGraw-Hill Education.
45) A random variable that is defined to be the total number of successes in n trials is a
________ random variable.
A) binomial
B) Poisson
C) hypergeometric
D) continuous
Answer: A
Explanation: This random variable also needs to be countable.
Difficulty: 1 Easy
Topic: The Binomial Distribution
Learning Objective: 06-03 Use the binomial distribution to compute probabilities.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
46) A discrete variable that can often be used to describe the number of occurrences of an event
over a specified interval of time or space is a ________ random variable.
A) Poisson
B) discrete
C) hypergeometric
D) continuous
Answer: A
Explanation: Poisson distribution deals with successes during a time interval.
Difficulty: 1 Easy
Topic: The Poisson Distribution
Learning Objective: 06-04 Use the Poisson distribution to compute probabilities.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
305
Copyright 2019 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior
written consent of McGraw-Hill Education.
47) The requirement that the probability of success remains constant from trial to trial is a
property of the ________ distribution.
A) binomial
B) Poisson
C) hypergeometric
D) continuous
Answer: A
Explanation: A previous success or failure does not dictate what will occur in the present trial.
Difficulty: 1 Easy
Topic: The Binomial Distribution
Learning Objective: 06-03 Use the binomial distribution to compute probabilities.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
48) The distribution whose mean is equal to its variance is the ________ distribution.
A) binomial
B) Poisson
C) hypergeometric
D) continuous
Answer: B
Explanation: This is the definition of a Poisson.
Difficulty: 1 Easy
Topic: The Poisson Distribution
Learning Objective: 06-04 Use the Poisson distribution to compute probabilities.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
306
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written consent of McGraw-Hill Education.
49) For a random variable X, the mean value of the squared deviations of its values from their
expected value is called its ________.
A) standard deviation
B) mean
C) probability
D) variance
Answer: D
Explanation: This can then be used to find the standard deviation, which is the positive square
root of the variance.
Difficulty: 2 Medium
Topic: Discrete Probability Distributions
Learning Objective: 06-02 Find a discrete probability distribution and compute its mean and
standard deviation.
Bloom's: Understand
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
50) When p = .5, the binomial distribution will ________ be symmetric.
A) always
B) sometimes
C) never
Answer: A
Explanation: This looks similar to a normal distribution.
Difficulty: 2 Medium
Topic: The Binomial Distribution
Learning Objective: 06-03 Use the binomial distribution to compute probabilities.
Bloom's: Understand
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
307
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written consent of McGraw-Hill Education.
51) Which of the following statements about the binomial distribution is not correct?
A) Each trial results in a success or failure.
B) Trials are independent of each other.
C) The probability of success remains constant from trial to trial.
D) The random variable of interest is continuous.
E) The experiment consists of n identical trials.
Answer: D
Explanation: The random variable of interest needs to be discrete.
Difficulty: 1 Easy
Topic: The Binomial Distribution
Learning Objective: 06-03 Use the binomial distribution to compute probabilities.
Bloom's: Remember
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
52) If n = 15 and p = .4, then the standard deviation of the binomial distribution is
A) 9.
B) 6.
C) 3.6.
D) 1.897.
E) 2.449.
Answer: D
Explanation: Standard deviation =
=
=
= 1.897
Difficulty: 3 Hard
Topic: The Binomial Distribution
Learning Objective: 06-03 Use the binomial distribution to compute probabilities.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
53) The equation for the variance of the binomial distribution is given by
A) px(1 − p)n−x.
B) np.
C) np(1 − p).
D)
.
Answer: C
Explanation: Where n is the number of trials and p is the probability of success.
Difficulty: 1 Easy
Topic: The Binomial Distribution
Learning Objective: 06-03 Use the binomial distribution to compute probabilities.
Bloom's: Remember
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
308
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written consent of McGraw-Hill Education.
54) The Securities and Exchange Commission has determined that the number of companies
listed on the NYSE declaring bankruptcy is approximately a Poisson distribution with a mean of
2.6 per month. Find the probability that exactly 4 bankruptcies occur next month.
A) .8774
B) .1414
C) .7736
D) .2640
Answer: B
Explanation: P(4) = e−2.6(2.6)4/4! (e = 2.71828)
Difficulty: 3 Hard
Topic: The Poisson Distribution
Learning Objective: 06-04 Use the Poisson distribution to compute probabilities.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
55) The Securities and Exchange Commission has determined that the number of companies
listed on the NYSE declaring bankruptcy is approximately a Poisson distribution with a mean of
2.6 per month. Find the probability that more than 1 bankruptcy occurs next month.
A) .1931
B) .9257
C) .7326
D) .4816
E) .2674
Answer: C
Explanation: P(1) = e−2.6(2.6)1/1! (e = 2.71828)
Difficulty: 3 Hard
Topic: The Poisson Distribution
Learning Objective: 06-04 Use the Poisson distribution to compute probabilities.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
309
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written consent of McGraw-Hill Education.
56) The Securities and Exchange Commission has determined that the number of companies
listed on the NYSE declaring bankruptcy is approximately a Poisson distribution with a mean of
2.6 per month. Find the probability that no more than one bankruptcy occurs next month.
A) .1931
B) .9257
C) .7326
D) .0742
E) .2674
Answer: E
Explanation: P(X = 0 or X = 1) = e−2.6(2.6)0/0! + e−2.6(2.6)1/1! (e = 2.71828)
Difficulty: 3 Hard
Topic: The Poisson Distribution
Learning Objective: 06-04 Use the Poisson distribution to compute probabilities.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
57) A fair die is rolled 10 times. What is the probability that an odd number (1, 3, or 5) will
occur fewer than 3 times?
A) .0547
B) .1172
C) .1550
D) .7752
E) .8450
Answer: A
Explanation: ΣP(X) = n!/[x!(n − x)!] × px(1 − p)n−x, for x = 1, 3, 5; or look up in binomial table
where x = 1 or 3 or 5 when p = .5 and n = 10.
Difficulty: 3 Hard
Topic: The Binomial Distribution
Learning Objective: 06-03 Use the binomial distribution to compute probabilities.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
310
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written consent of McGraw-Hill Education.
58) A fair die is rolled 10 times. What is the probability that an even number (2, 4, or 6) will
occur between 2 and 4 times inclusive?
A) .6123
B) .1709
C) .1611
D) .3662
E) .3223
Answer: D
Explanation: ΣP(X) = n!/[x!(n − x)!] × px(1 − p)n−x, for x = 2, 4, 6; or look up in binomial table,
where x = 2 or 4 or 6 when p = .5 and n = 10.
Difficulty: 3 Hard
Topic: The Binomial Distribution
Learning Objective: 06-03 Use the binomial distribution to compute probabilities.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
59) A fair die is rolled 10 times. What is the average number of even number outcomes?
A) 3
B) 4
C) 5
D) 6
E) 7
Answer: C
Explanation: Binomial mean = μ = np = 10(.5) = 5
Difficulty: 3 Hard
Topic: The Binomial Distribution
Learning Objective: 06-03 Use the binomial distribution to compute probabilities.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
311
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written consent of McGraw-Hill Education.
60) A fair die is rolled 36 times. What is the standard deviation of the even number (2, 4, or 6)
outcomes?
A) 18
B) 9
C) 4.243
D) 3
E) 1.732
Answer: D
Explanation: Binomial standard deviation = σ =
=
=
=3
Difficulty: 2 Medium
Topic: The Binomial Distribution
Learning Objective: 06-03 Use the binomial distribution to compute probabilities.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
61) The manager of the local grocery store has determined that, on average, 4 customers use the
service desk every half-hour. Assume that the number of customers using the service desk has a
Poisson distribution. What is the probability that during a randomly selected half-hour period,
exactly 2 customers use the service desk?
A) .1483
B) .0916
C) .1465
D) .9084
E) .7619
Answer: C
Explanation: P(2) = e−4(4)2/2! (e = 2.71828)
Difficulty: 3 Hard
Topic: The Poisson Distribution
Learning Objective: 06-04 Use the Poisson distribution to compute probabilities.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
312
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written consent of McGraw-Hill Education.
62) The manager of the local grocery store has determined that, on average, 4 customers use the
service desk every half-hour. Assume that the number of customers using the service desk has a
Poisson distribution. What is the probability that during a randomly selected half-hour period, no
more than 2 customers use the service desk?
A) .2381
B) .1465
C) .7619
D) .9084
E) .0916
Answer: A
Explanation: P(x < 3) = Σ e−μ(μ)x/x!, for x = 0, 1, 2 (e = 2.71828)
Difficulty: 3 Hard
Topic: The Poisson Distribution
Learning Objective: 06-04 Use the Poisson distribution to compute probabilities.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
63) The probability that a given computer chip will fail is .02. Find the probability that of 5
delivered chips, exactly 2 chips will fail.
A) .9962
B) .0999
C) .0038
D) .0000
Answer: C
Explanation: P(X) = n!/[x!(n − x)!] × px(1 − p)n−x, for x = 2, n = 5, p = .02
Difficulty: 2 Medium
Topic: The Binomial Distribution
Learning Objective: 06-03 Use the binomial distribution to compute probabilities.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
313
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written consent of McGraw-Hill Education.
64) According to a survey of adults, 64 percent have money in a bank savings account. If we
were to survey 50 randomly selected adults, find the mean number of adults who would have
bank savings accounts.
A) 12
B) 22
C) 32
D) 42
Answer: C
Explanation: Mean = np = 50(.64) = 32
Difficulty: 3 Hard
Topic: Discrete Probability Distributions
Learning Objective: 06-03 Use the binomial distribution to compute probabilities.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
65) In the most recent election, 19 percent of all eligible college students voted. If a random
sample of 20 students were surveyed, find the probability that exactly half voted in the election.
A) .0000
B) .0014
C) .0004
D) .0017
Answer: B
Explanation: P(X) = n!/[x!(n − x)!] × px(1 − p)n−x, for x = 10, when p = .19 and n = 20.
Difficulty: 3 Hard
Topic: The Binomial Distribution
Learning Objective: 06-03 Use the binomial distribution to compute probabilities.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
314
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written consent of McGraw-Hill Education.
66) In the most recent election, 19 percent of all eligible college students voted. If a random
sample of 20 students were surveyed, find the probability that none of the students voted.
A) .0000
B) .0014
C) .0148
D) .9852
Answer: C
Explanation: P(X) = n!/[x!(n − x)!] × px(1 − p)n−x, for x = 0 when p = .19 and n = 20.
Difficulty: 2 Medium
Topic: The Binomial Distribution
Learning Objective: 06-03 Use the binomial distribution to compute probabilities.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
67) Of all individual tax returns, 37 percent include errors made by the taxpayer. If IRS
examiners are assigned randomly selected returns in batches of 12, find the mean and standard
deviation for the number of erroneous returns per batch.
A) μ = 2.80, σ = 1.67
B) μ = 4.44, σ = 1.67
C) μ = 4.44, σ = 2.80
D) μ = 7.56, σ = 2.80
Answer: B
Explanation: Mean = np = 12(.37) = 4.44
Standard Deviation =
=
= 1.67
Difficulty: 2 Medium
Topic: The Binomial Distribution
Learning Objective: 06-03 Use the binomial distribution to compute probabilities.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
315
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written consent of McGraw-Hill Education.
68) In a study conducted for the state Department of Education, 30 percent of the teachers who
left teaching did so because they were laid off. Assume that we randomly select 10 teachers who
have recently left their profession. Find the probability that exactly 4 of them were laid off.
A) .6496
B) .8497
C) .2001
D) .1503
Answer: C
Explanation: P(X) = n!/[x!(n − x)!] × px(1 − p)n−x, for x = 4, when p = .3 and n = 10
Difficulty: 2 Medium
Topic: The Binomial Distribution
Learning Objective: 06-03 Use the binomial distribution to compute probabilities.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
69) An appliance manufacturer gives a warranty and 95 percent of its appliances do not require
repair before the warranty expires. An organization buys 10 of these appliances. Calculate an
interval that contains 95.44 percent of all the appliances that will not require repair.
A) [8.12, 10.88]
B) [7.43, 11.57]
C) [8.81, 10.19]
D) [8.55, 10.45]
Answer: A
Explanation: μ = np = 10(.95) = 9.5
σ=
=
= .6892
95.44% is a 2-standard-deviation interval: [μ ± 2σ] = [9.5 ± 2(.6892)]
= [8.12, 10.88]
Difficulty: 3 Hard
Topic: The Binomial Distribution
Learning Objective: 06-03 Use the binomial distribution to compute probabilities.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
316
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written consent of McGraw-Hill Education.
70) A manufacturer tested a sample of semiconductor chips and found that 35 were defective and
190 were good. If additional tests are to be conducted with random samples of 160
semiconductor chips, find the mean for the number of defects in these groups of 160 (rounded to
the nearest whole number).
A) 56
B) 35
C) 29
D) 25
Answer: D
Explanation: Sample size = 35 + 190 = 225
p = 35/225 = .156
Mean of 160 groups = 160(.156) = 24.96, rounded to 25
Difficulty: 3 Hard
Topic: The Poisson Distribution
Learning Objective: 06-04 Use the Poisson distribution to compute probabilities.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
71) A study conducted by a local university found that 25 percent of college freshmen support
increased spending on environmental issues. If 6 college freshmen are randomly selected, find
the probability that fewer than 4 support increased spending on environmental issues.
A) .0330
B) .0046
C) .9624
D) .9954
Answer: C
Explanation: Σ P(X) = n!/[x!(n − x)!] × px(1 − p)n−x, for x = 0, 1, 2, 3 when p = .25 and n = 6.
Difficulty: 2 Medium
Topic: The Binomial Distribution
Learning Objective: 06-03 Use the binomial distribution to compute probabilities.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
317
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written consent of McGraw-Hill Education.
72) A study conducted by a local university found that 25 percent of college freshmen support
increased spending on environmental issues. If 6 college freshmen are randomly selected, find
the probability that exactly 3 support increased spending on environmental issues.
A) .8306
B) .1318
C) .0376
D) .9624
Answer: B
Explanation: P(X) = n!/[x!(n − x)!] × px(1 − p)n−x, for x = 3 when p = .25 and n = 6.
Difficulty: 2 Medium
Topic: The Binomial Distribution
Learning Objective: 06-03 Use the binomial distribution to compute probabilities.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
73) A study conducted by a local university found that 25 percent of college freshmen support
increased spending on environmental issues. If 6 college freshmen are randomly selected, find
the probability that only 1 supports increased spending on environmental issues.
A) .3559
B) .1780
C) .3560
D) .5339
Answer: C
Explanation: P(X) = n!/[x!(n − x)!] × px(1 − p)n−x, for x = 1 when p = .25 and n = 6.
Difficulty: 2 Medium
Topic: The Binomial Distribution
Learning Objective: 06-03 Use the binomial distribution to compute probabilities.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
318
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written consent of McGraw-Hill Education.
74) A multiple-choice test has 30 questions and each one has five possible answers, of which
only one is correct. If all answers were guesses, find the probability of getting exactly four
correct answers.
A) .1227
B) .1325
C) .0604
D) .0374
Answer: B
Explanation: Probability of getting question correct = .2. Four successes in 30 trials. Treat as a
binomial.
P(X) = n!/[x!(n − x)!] × px(1 − p)n−x, for x = 4, when p = .20 and n = 30.
Difficulty: 2 Medium
Topic: The Binomial Distribution
Learning Objective: 06-03 Use the binomial distribution to compute probabilities.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
75) The J.O. Supplies Company buys calculators from a non-U.S. supplier. The probability of a
defective calculator is 10 percent. If 3 calculators are selected at random, what is the probability
that one of the calculators will be defective?
A) .9720
B) .0280
C) .2430
D) .7290
Answer: C
Explanation:
= .243
Difficulty: 2 Medium
Topic: The Binomial Distribution
Learning Objective: 06-03 Use the binomial distribution to compute probabilities.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
319
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written consent of McGraw-Hill Education.
76) The J.O. Supplies Company buys calculators from a non-U.S. supplier. The probability of a
defective calculator is 10 percent. If 10 calculators are selected at random, what is the probability
that 3 or more of the calculators will be defective?
A) .0702
B) .0574
C) .9298
D) .0128
Answer: A
Explanation: P(X ≥ 3) = 1 − P(X ≤ 2) = 1 − .9298 = .0702
Difficulty: 3 Hard
Topic: The Binomial Distribution
Learning Objective: 06-03 Use the binomial distribution to compute probabilities.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
77) The J.O. Supplies Company buys calculators from a non-U.S. supplier. The probability of a
defective calculator is 10 percent. If 100 calculators are selected at random, what is the expected
number of defectives?
A) 9
B) 90
C) 10
D) 95
Answer: C
Explanation: E[X] = μx = (.10)(100) = 10
Difficulty: 2 Medium
Topic: The Binomial Distribution
Learning Objective: 06-03 Use the binomial distribution to compute probabilities.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
320
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written consent of McGraw-Hill Education.
78) The J.O. Supplies Company buys calculators from a non-U.S. supplier. The probability of a
defective calculator is 10 percent. If 100 calculators are selected at random, what is the standard
deviation of the number of defective calculators?
A) 9.00
B) 3.17
C) 9.49
D) 3.00
Answer: D
Explanation:
=
=3
Difficulty: 2 Medium
Topic: The Binomial Distribution
Learning Objective: 06-03 Use the binomial distribution to compute probabilities.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
79) Historical data show that the average number of patient arrivals at the intensive care unit of
General Hospital is 3 patients every two hours. Assume that the patient arrivals are distributed
according to a Poisson distribution. Determine the probability of 6 patients arriving in a fivehour period.
A) .136
B) .109
C) .246
D) .001
Answer: A
Explanation: P(X = 6) =
= .1359
Difficulty: 2 Medium
Topic: The Poisson Distribution
Learning Objective: 06-04 Use the Poisson distribution to compute probabilities.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
321
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written consent of McGraw-Hill Education.
80) Historical data show that the average number of patient arrivals at the intensive care unit of
General Hospital is 3 patients every 2 hours. Assume that the patient arrivals are distributed
according to a Poisson distribution. Determine the probability of at least 4 but no more than 8
patients arriving in a three-hour period.
A) .3813
B) .5711
C) .4276
D) .7861
E) .6174
Answer: E
Explanation:
P(4 ≤ X ≤ 8) = P(X = 8) + P(X = 7) + P(X = 6) + P(X = 5) + P(X = 4)
= (.0463) + (.0824) + (.1281) + (.1708) + (.1898) = .6174
Difficulty: 2 Medium
Topic: The Poisson Distribution
Learning Objective: 06-04 Use the Poisson distribution to compute probabilities.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
81) The probability distribution of X is
X
3
4
5
6
P(X)
1/8
1/8
3/8
3/8
What is the expected value of X?
A) 1.0
B) 5.0
C) 2.25
D) 2.24
Answer: B
Explanation:
E[X] = 3
+4
+5
+6
=
= 5.0
Difficulty: 2 Medium
Topic: Discrete Probability Distributions
Learning Objective: 06-02 Find a discrete probability distribution and compute its mean and
standard deviation.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
322
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written consent of McGraw-Hill Education.
82) The probability distribution of X is
X
3
4
5
6
P(X)
1/8
1/8
3/8
3/8
What is the variance of X?
A) 1.0
B) 5.0
C) 2.25
D) 2.24
Answer: A
Explanation:
E[X] = 3
=
+4
+5
+
+6
=
+
= 5.0
+
=1
Difficulty: 2 Medium
Topic: Discrete Probability Distributions
Learning Objective: 06-02 Find a discrete probability distribution and compute its mean and
standard deviation.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
323
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written consent of McGraw-Hill Education.
83) Assume the number of trucks passing an intersection has a Poisson distribution with a mean
of 5 trucks per minute. What is the probability of 0 or 1 trucks in one minute?
A) .0404
B) .0337
C) .9596
D) .0067
Answer: A
Explanation:
+
= .0404
Difficulty: 2 Medium
Topic: The Poisson Distribution
Learning Objective: 06-04 Use the Poisson distribution to compute probabilities.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
84) A vaccine is 95 percent effective. What is the probability that it is not effective for 1 and
only 1 individual out of 20 individuals?
A) .2642
B) .6415
C) .3584
D) .3774
Answer: D
Explanation: (20)(.95)19(.05)1 = .3774
Difficulty: 2 Medium
Topic: The Binomial Distribution
Learning Objective: 06-03 Use the binomial distribution to compute probabilities.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
324
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written consent of McGraw-Hill Education.
85) A vaccine is 95 percent effective. What is the probability that it is not effective for more than
1 out of 20 individuals?
A) .7359
B) .2641
C) .6415
D) .3773
Answer: C
Explanation:
P(X ≥ 2) = 1 − [P(X = 0) + p(X = 1)]
= 1 − [.3585 + .3774] = .2641
Difficulty: 2 Medium
Topic: The Binomial Distribution
Learning Objective: 06-03 Use the binomial distribution to compute probabilities.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
86) If the probability of a success on a single trial is .2, what is the probability of obtaining 3
successes in 10 trials if the number of successes is binomial?
A) .1209
B) .6778
C) .1208
D) .2013
Answer: D
Explanation:
= .2013
Difficulty: 3 Hard
Topic: The Binomial Distribution
Learning Objective: 06-03 Use the binomial distribution to compute probabilities.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
325
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written consent of McGraw-Hill Education.
87) The number of calls coming into a call center follows a Poisson distribution with a mean of
120 calls per hour. What is the probability of no calls in a one-minute interval?
A) 0
B) .1353
C) .4060
D) .3679
Answer: B
Explanation:
P(X = 0) =
=
= .1353
Difficulty: 3 Hard
Topic: The Poisson Distribution
Learning Objective: 06-04 Use the Poisson distribution to compute probabilities.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
88) If x is a Poisson random variable with a mean of 10, what is the probability that x is greater
than 6?
A) .9329
B) .1301
C) .8698
D) .0631
Answer: C
Explanation: P(X ≥ 7) = 1 − P(X ≤ 6) = 1 − (.1302) = .8698
Difficulty: 3 Hard
Topic: The Poisson Distribution
Learning Objective: 06-04 Use the Poisson distribution to compute probabilities.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
326
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written consent of McGraw-Hill Education.
89) Three candidates run for different offices in different cities. Each has a one in three chance of
being elected in his/her city. What is the probability that at least one of them will be elected?
A) .4444
B) .7037
C) .3300
D) .6670
Answer: B
Explanation:
P(X ≥ 1) = 1 − P(X = 0) P(X = 0) =
=1−
=
=
P(X ≥ 1)
= .7037
Difficulty: 3 Hard
Topic: The Binomial Distribution
Learning Objective: 06-03 Use the binomial distribution to compute probabilities.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
90) A test has 6 multiple-choice questions, each with 4 choices. What is the probability of
guessing 5 or more questions correctly?
A) .0044
B) .0002
C) .9954
D) .0046
Answer: D
Explanation:
P(X ≥ 5) = P(X = 5) + P(X = 6)
= (.0044) + (.0002) = .0046
Difficulty: 3 Hard
Topic: The Binomial Distribution
Learning Objective: 06-03 Use the binomial distribution to compute probabilities.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
327
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written consent of McGraw-Hill Education.
91) If x is a Poisson random variable with a mean of 10, what is the probability that x is greater
than or equal to 2?
A) .9972
B) .0028
C) .9995
D) .0005
Answer: C
Explanation: P(X ≥ 2) = 1 − [P(X = 0) + P(X = 1)]
= 1 − (0 + .0005) = .9995
Difficulty: 3 Hard
Topic: The Poisson Distribution
Learning Objective: 06-04 Use the Poisson distribution to compute probabilities.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
92) If x is a Poisson random variable with a mean of 10, what is the probability that x is equal to
8?
A) .1126
B) .2202
C) .3328
D) .7797
Answer: A
Explanation:
P(X = 8) =
= .1126
Difficulty: 3 Hard
Topic: The Poisson Distribution
Learning Objective: 06-04 Use the Poisson distribution to compute probabilities.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
328
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written consent of McGraw-Hill Education.
93) Twenty coins are tossed. What is the probability of getting exactly 10 heads?
A) .4119
B) .5881
C) .5000
D) .1762
Answer: D
Explanation:
P(X = 10) =
= .1762
Difficulty: 3 Hard
Topic: The Binomial Distribution
Learning Objective: 06-03 Use the binomial distribution to compute probabilities.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
94) Determine the probability that a 3 will appear twice, if a single fair die is rolled 10 times.
A) .7752
B) .2907
C) .1550
D) .4845
Answer: B
Explanation:
P(X = 2) =
= .2907
Difficulty: 3 Hard
Topic: The Binomial Distribution
Learning Objective: 06-03 Use the binomial distribution to compute probabilities.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
329
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written consent of McGraw-Hill Education.
95) During off-hours, cars arrive at a tollbooth on the East-West toll road at an average rate of .5
cars per minute. The arrivals are distributed according to a Poisson distribution. What is the
probability that during the next minute, three cars will arrive?
A) .9856
B) .3033
C) .0126
D) .8956
Answer: C
Explanation:
P(X = 3) =
=
= .0126
Difficulty: 2 Medium
Topic: The Poisson Distribution
Learning Objective: 06-04 Use the Poisson distribution to compute probabilities.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
96) During off-hours, cars arrive at a tollbooth on the East-West toll road at an average rate of .5
cars per minute. The arrivals are distributed according to a Poisson distribution. What is the
probability that during the next five minutes, three cars will arrive?
A) .2138
B) .5438
C) .0126
D) .0002
Answer: A
Explanation:
P(X = 3) =
=
= .2138
Difficulty: 2 Medium
Topic: The Poisson Distribution
Learning Objective: 06-04 Use the Poisson distribution to compute probabilities.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
330
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written consent of McGraw-Hill Education.
97) For a binomial process, the probability of success is 40 percent and the number of trials is 5.
Find the expected value.
A) 5.0
B) 1.2
C) 2.0
D) 1.1
Answer: C
Explanation: E[X] = (5)(.40) = 2
Difficulty: 2 Medium
Topic: The Binomial Distribution
Learning Objective: 06-03 Use the binomial distribution to compute probabilities.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
98) For a binomial process, the probability of success is 40 percent and the number of trials is 5.
Find the variance.
A) 5.0
B) 1.2
C) 2.0
D) 1.1
Answer: B
Explanation: σ2x = (5)(.4)(.6) = 1.2
Difficulty: 2 Medium
Topic: The Binomial Distribution
Learning Objective: 06-03 Use the binomial distribution to compute probabilities.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
331
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written consent of McGraw-Hill Education.
99) For a binomial process, the probability of success is 40 percent and the number of trials is 5.
Find the standard deviation.
A) 5.0
B) 1.2
C) 2.0
D) 1.1
Answer: D
Explanation:
=
= 1.0954
Difficulty: 2 Medium
Topic: The Binomial Distribution
Learning Objective: 06-03 Use the binomial distribution to compute probabilities.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
100) For a binomial process, the probability of success is 40 percent and the number of trials is 5.
Find P(X ≤ 1).
A) .2592
B) .6630
C) .0778
D) .3370
Answer: D
Explanation:
P(X ≤ 1) = P(X = 0) + P(X = 1)
= (.0778) + (.2592) = .337
Difficulty: 2 Medium
Topic: The Binomial Distribution
Learning Objective: 06-03 Use the binomial distribution to compute probabilities.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
332
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written consent of McGraw-Hill Education.
101) For a binomial process, the probability of success is 40 percent and the number of trials is 5.
Find P(X > 4).
A) .0102
B) .0778
C) .0870
D) .9898
Answer: A
Explanation: P(X = 5) = (.4)5 = .0102
Difficulty: 2 Medium
Topic: The Binomial Distribution
Learning Objective: 06-03 Use the binomial distribution to compute probabilities.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
102) Consider a Poisson distribution with an average of 3 customers per minute at the local
grocery store. Determine the expected number of customer arrivals for a five-minute period.
A) 15
B) 3
C) 243
D) 125
Answer: A
Explanation: μ = (3)(5) = 15
Difficulty: 3 Hard
Topic: The Poisson Distribution
Learning Objective: 06-04 Use the Poisson distribution to compute probabilities.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
333
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written consent of McGraw-Hill Education.
103) Consider a Poisson distribution with an average of 3 customers per minute at the local
grocery store. If X = the number of arrivals per minute, find the expected value of X.
A) 3
B) 9
C) 1.5
D) 1.7
Answer: A
Explanation: The expected value of X would be the average in the minute, or 3.
Difficulty: 3 Hard
Topic: The Poisson Distribution
Learning Objective: 06-04 Use the Poisson distribution to compute probabilities.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
104) Consider a Poisson distribution with an average of 3 customers per minute at the local
grocery store. If X = the number of arrivals per minute, find the variance of X.
A) 3
B) 9
C) 1.5
D) 1.7
Answer: A
Explanation:
=μ=3
Difficulty: 3 Hard
Topic: The Poisson Distribution
Learning Objective: 06-04 Use the Poisson distribution to compute probabilities.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
334
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written consent of McGraw-Hill Education.
105) Consider a Poisson distribution with an average of 4 customers per minute at the local
grocery store. If X = the number of arrivals per minute, find the standard deviation of X.
A) 2
B) 4
C) 16
D) 1.5
Answer: A
Explanation: σx =
= 2.00
Difficulty: 3 Hard
Topic: The Poisson Distribution
Learning Objective: 06-04 Use the Poisson distribution to compute probabilities.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
106) Consider a Poisson distribution with an average of 3 customers per minute at the local
grocery store. If X = the number of arrivals per minute, find the probability of 10 customers or
fewer arriving within a minute.
A) .9998
B) .9990
C) .0008
D) .0002
Answer: A
Explanation: P(X ≤ 10) = 1 − P(X ≥ 11) = 1 − .0002 = .9998
Difficulty: 2 Medium
Topic: The Poisson Distribution
Learning Objective: 06-04 Use the Poisson distribution to compute probabilities.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
335
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written consent of McGraw-Hill Education.
107) Consider a Poisson distribution with an average of 3 customers per minute at the local
grocery store. If X = the number of arrivals per minute, find the probability of more than 7
customers arriving within a minute.
A) .0216
B) .0081
C) .9881
D) .0118
Answer: D
Explanation: P(X ≥ 8) = .0081 + .0027 + .0008 + .0002 = .0118
Difficulty: 2 Medium
Topic: The Poisson Distribution
Learning Objective: 06-04 Use the Poisson distribution to compute probabilities.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
108) Consider a Poisson distribution with an average of 3 customers per minute at the local
grocery store. If X = the number of arrivals per minute, find the probability of 3 customers
arriving within a minute.
A) 1.00
B) .4232
C) .2240
D) .3734
Answer: C
Explanation:
P(X = 3) =
=
= .224
Difficulty: 2 Medium
Topic: The Poisson Distribution
Learning Objective: 06-04 Use the Poisson distribution to compute probabilities.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
336
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written consent of McGraw-Hill Education.
109) One die is thrown. What is the expected value of the number of dots on the top face of the
die?
A) 1.0
B) 3.5
C) 4.0
D) 3.0
Answer: B
Explanation:
E[X] = 1
+2
+3
+4
+5
+6
Difficulty: 2 Medium
Topic: Discrete Probability Distributions
Learning Objective: 06-02 Find a discrete probability distribution and compute its mean and
standard deviation.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
110) X has the following probability distribution.
X
P(X)
−2
0.2
−1
0.2
9
0.2
1
0.2
2
0.2
Compute the expected value of X.
A) 1.3
B) 1.0
C) 2.4
D) 1.8
Answer: D
Explanation: E[X] = (−2)(.2) + (−1)(.2) + (1)(.2) + (2)(.2) + (9)(.2) = 1.8
Difficulty: 2 Medium
Topic: Discrete Probability Distributions
Learning Objective: 06-02 Find a discrete probability distribution and compute its mean and
standard deviation.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
337
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written consent of McGraw-Hill Education.
111) X has the following probability distribution P(X).
X
P(X)
1
0.1
2
0.5
3
0.2
4
0.2
Compute the expected value of X.
A) 2.5
B) 1.0
C) 1.6
D) .6
Answer: A
Explanation: E[X] = (1)(.1) + (2)(.5) + (3)(.2) + (4)(.2) = 2.5
Difficulty: 2 Medium
Topic: Discrete Probability Distributions
Learning Objective: 06-02 Find a discrete probability distribution and compute its mean and
standard deviation.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
112) X has the following probability distribution P(X).
X
P(X)
1
0.1
2
0.5
3
0.2
4
0.2
Compute the variance value of X.
A) 1.58
B) .955
C) .850
D) .625
Answer: C
Explanation:
E[X] = (1)(.1) + (2)(.5) + (3)(.2) + (4)(.2) = 2.5
σ2x =
(.1) +
(.5) +
(.2) +
(.2) = .85
Difficulty: 2 Medium
Topic: Discrete Probability Distributions
Learning Objective: 06-02 Find a discrete probability distribution and compute its mean and
standard deviation.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
338
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written consent of McGraw-Hill Education.
113) Historical data for a local manufacturing company show that the average number of defects
per product produced is 2. In addition, the number of defects per unit is distributed according to a
Poisson distribution. What is the probability that there will be a total of 7 defects on four units?
A) .6063
B) .0902
C) .0034
D) .1396
Answer: D
Explanation:
P(X = 7) =
=
= .1396
Difficulty: 2 Medium
Topic: The Poisson Distribution
Learning Objective: 06-04 Use the Poisson distribution to compute probabilities.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
114) Historical data for a local manufacturing company show that the average number of defects
per product produced is 2. In addition, the number of defects per unit is distributed according to a
Poisson distribution. A batch has just been completed. What is the probability that the first three
units manufactured in this batch will contain at least a total of 4 defects?
A) .8488
B) .7149
C) .1512
D) .2851
Answer: A
Explanation:
P(X ≥ 4) = 1 − [P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)]
= 1 − (.0025 + .0149 + .0446 + .0892) = .8488
Difficulty: 2 Medium
Topic: The Poisson Distribution
Learning Objective: 06-04 Use the Poisson distribution to compute probabilities.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
339
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written consent of McGraw-Hill Education.
115) Historical data for a local manufacturing company show that the average number of defects
per product produced is 2. In addition, the number of defects per unit is distributed according to a
Poisson distribution. Determine the standard deviation of the number of defects for 32 units.
A) 2
B) 32
C) 64
D) 8
Answer: D
Explanation:
=
=8
Difficulty: 1 Easy
Topic: The Poisson Distribution
Learning Objective: 06-04 Use the Poisson distribution to compute probabilities.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
116) Consider the experiment of tossing a fair coin three times and observing the number of
heads that result (X = number of heads). Determine the expected number of heads.
A) 1.5
B) 1.0
C) 2.0
D) 1.1
Answer: A
Explanation:
E[X] =
=0
+ (1)
+ (2)
+ (3)
= 1.5
Difficulty: 3 Hard
Topic: The Binomial Distribution
Learning Objective: 06-03 Use the binomial distribution to compute probabilities.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
340
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written consent of McGraw-Hill Education.
117) Consider the experiment of tossing a fair coin three times and observing the number of
heads that result (X = number of heads). What is the variance for this distribution?
A) 1.5
B) 1.22
C) .75
D) .87
Answer: C
Explanation:
E[X] =
=0
=
+ (1)
+ (2)
+
+ (3)
+
= 1.5
+
= .75
Difficulty: 3 Hard
Topic: Discrete Probability Distributions
Learning Objective: 06-02 Find a discrete probability distribution and compute its mean and
standard deviation.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
118) Consider the experiment of tossing a fair coin three times and observing the number of
heads that result (X = number of heads). What is the standard deviation for this distribution?
A) 1.5
B) 1.22
C) .75
D) .87
Answer: D
Explanation:
E[X] =
=
=0
+ (1)
+
+ (2)
+ (3)
+
= 1.5
+
= .75
=
= .866
Difficulty: 3 Hard
Topic: Discrete Probability Distributions
Learning Objective: 06-02 Find a discrete probability distribution and compute its mean and
standard deviation.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
341
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written consent of McGraw-Hill Education.
119) If you were asked to play a game in which you tossed a fair coin three times and were given
$2 for every head you threw, how much would you expect to win on average?
A) $3
B) $2
C) $6
D) $9
Answer: A
Explanation:
Expected return = 0
+ ($2)(1)
+ ($2)(2)
+ ($2)(3)
= 3.0
Difficulty: 3 Hard
Topic: Discrete Probability Distributions
Learning Objective: 06-02 Find a discrete probability distribution and compute its mean and
standard deviation.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
120) A pharmaceutical company has determined that if a new cholesterol-reducing drug is
manufactured and introduced to the market, the following probability distribution will describe
the contribution of this drug to their profits during the next six months.
Profit Contribution
−$3,000,000
(negative profit)
$5,000,000
$2,000,000
Probability of Profit Contribution
0.20
0.50
0.30
The company management has decided to market this product if the expected contribution to
profit for the next six months is more than $1,000,000. Based on the information given above,
should the company begin manufacturing the new drug? Explain your answer.
A) Yes, begin manufacturing.
B) No, do not begin manufacturing.
Answer: A
Explanation: μx = .2(−$3,000,000) + .5($5,000,000) + .3($2,000,000) = $2,500,000
$2,500,000 > $1,000,000
Difficulty: 2 Medium
Topic: Discrete Probability Distributions
Learning Objective: 06-02 Find a discrete probability distribution and compute its mean and
standard deviation.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
342
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written consent of McGraw-Hill Education.
121) According to data from the state blood program, 40 percent of all individuals have group A
blood. If six individuals give blood, find the probability that none of the individuals has group A
blood.
A) .0041
B) .0410
C) .4000
D) .0467
Answer: D
Explanation: P(x = 0) = .0467
Difficulty: 1 Easy
Topic: The Binomial Distribution
Learning Objective: 06-03 Use the binomial distribution to compute probabilities.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
122) According to data from the state blood program, 40 percent of all individuals have group A
blood. If six individuals give blood, find the probability that exactly three of the individuals have
group A blood.
A) .5443
B) .2765
C) .1792
D) .0041
Answer: B
Explanation: P(x = 3) = .2765
Difficulty: 1 Easy
Topic: The Binomial Distribution
Learning Objective: 06-03 Use the binomial distribution to compute probabilities.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
343
Copyright 2019 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior
written consent of McGraw-Hill Education.
123) According to data from the state blood program, 40 percent of all individuals have group A
blood. If six individuals give blood, find the probability that at least 3 of the individuals have
group A blood.
A) .8208
B) .5443
C) .4557
D) .1792
Answer: C
Explanation: P(x ≥ 3) = p(x = 3) + p(x = 4) + p(x = 5) + p(x = 6) = .4557
Difficulty: 2 Medium
Topic: The Binomial Distribution
Learning Objective: 06-03 Use the binomial distribution to compute probabilities.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
124) According to data from the state blood program, 40 percent of all individuals have group A
blood. If six individuals give blood, find the mean number of individuals having group A blood.
A) 1.2
B) 1.55
C) 1.44
D) 2.4
Answer: D
Explanation: μx = np = (6)(.4) = 2.4
Difficulty: 1 Easy
Topic: The Binomial Distribution
Learning Objective: 06-03 Use the binomial distribution to compute probabilities.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
344
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written consent of McGraw-Hill Education.
125) According to data from the state blood program, 40 percent of all individuals have group A
blood. Suppose that of six randomly selected individuals, three have group A blood. Would you
believe the data from the state blood program?
A) Yes, probability is > .05.
B) Yes, probability is < .05.
C) No
Answer: A
Explanation: Yes, the probability is greater than 0.05, and therefore we do not reject the null
hypothesis.
Difficulty: 2 Medium
Topic: The Binomial Distribution
Learning Objective: 06-03 Use the binomial distribution to compute probabilities.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
126) A lawyer believes that the probability is .3 that she can win a discrimination suit. If she
wins the case, she will make $400,000; but if she loses, she gets nothing. Assume that she has to
spend $75,000 preparing the case. What is her expected gain?
A) $325,000
B) $45,000
C) $150,000
D) $22,500
Answer: B
Explanation: μx = .7(−75,000) + .3(325,000) = −52,500 + 97,500 = 45,000
Difficulty: 3 Hard
Topic: Discrete Probability Distributions
Learning Objective: 06-02 Find a discrete probability distribution and compute its mean and
standard deviation.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
345
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written consent of McGraw-Hill Education.
127) The internal auditor for your company believes that 10 percent of your invoices contain
errors. To check this theory, 20 invoices are randomly selected, and 5 are found to have errors.
What is the probability that of the 20 invoices selected, 5 or more would contain errors if the
theory is valid?
A) .0433
B) .0319
C) .9567
D) .8660
Answer: A
Explanation: P(x ≥ 5) = .0319 + .0089 + .0020 + .0004 + .0001 = .0433
Difficulty: 3 Hard
Topic: The Binomial Distribution
Learning Objective: 06-03 Use the binomial distribution to compute probabilities.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
128) An important part of the customer service responsibilities of a cable company is the speed
with which service troubles can be repaired. Historically, the data show that the likelihood is .75
that troubles in a residential service can be repaired on the same day. For the first five troubles
reported on a given day, what is the probability that all five will be repaired on the same day?
A) .0010
B) .6328
C) .7627
D) .2373
Answer: D
Explanation: P(x = 5) = .2373
Difficulty: 3 Hard
Topic: The Binomial Distribution
Learning Objective: 06-03 Use the binomial distribution to compute probabilities.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
346
Copyright 2019 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior
written consent of McGraw-Hill Education.
129) An important part of the customer service responsibilities of a cable company is the speed
with which service troubles can be repaired. Historically, the data show that the likelihood is .75
that troubles in a residential service can be repaired on the same day. For the first five troubles
reported on a given day, what is the probability that fewer than two troubles will be repaired on
the same day?
A) .6328
B) .0879
C) .0156
D) .1035
Answer: C
Explanation: P(x < 2) = P(x = 0) + P(x = 1) = .0156
Difficulty: 2 Medium
Topic: The Binomial Distribution
Learning Objective: 06-03 Use the binomial distribution to compute probabilities.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
130) An important part of the customer service responsibilities of a cable company is the speed
with which service troubles can be repaired. Historically, the data show that the likelihood is .75
that troubles in a residential service can be repaired on the same day. For the first five troubles
reported on a given day, what is the probability that at least three troubles will be repaired on the
same day?
A) .1035
B) .3672
C) .6328
D) .8965
Answer: D
Explanation: P(x ≥ 3) = 1 − (P ≤ 2) = .8965
Difficulty: 2 Medium
Topic: The Binomial Distribution
Learning Objective: 06-03 Use the binomial distribution to compute probabilities.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
347
Copyright 2019 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior
written consent of McGraw-Hill Education.
131) An important part of the customer service responsibilities of a cable company is the speed
with which service troubles can be repaired. Historically, the data show that the likelihood is .75
that troubles in a residential service can be repaired on the same day. For the first five troubles
reported on a given day, find the mean number of troubles repaired on the same day.
A) 3.75
B) .94
C) 1.94
D) 2.50
Answer: A
Explanation: μx = np = (5)(.75) = 3.75
Difficulty: 1 Easy
Topic: The Binomial Distribution
Learning Objective: 06-03 Use the binomial distribution to compute probabilities.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
132) The Post Office has established a record in a major midwestern city for delivering 90
percent of its local mail the next working day. If you mail eight local letters, what is the
probability that all of them will be delivered the next day?
A) 1.0
B) .4305
C) .8131
D) .5695
Answer: B
Explanation: P(x = 8) = .4305
Difficulty: 1 Easy
Topic: The Binomial Distribution
Learning Objective: 06-03 Use the binomial distribution to compute probabilities.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
348
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written consent of McGraw-Hill Education.
133) The Post Office has established a record in a major midwestern city for delivering 90
percent of its local mail the next working day. If you mail eight local letters, what is the average
number you expect to be delivered the next day?
A) 3.6
B) 4.0
C) 7.2
D) 2.7
Answer: C
Explanation: μx = np = (8)(.9) = 7.2
Difficulty: 1 Easy
Topic: The Binomial Distribution
Learning Objective: 06-03 Use the binomial distribution to compute probabilities.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
134) The Post Office has established a record in a major midwestern city for delivering 90
percent of its local mail the next working day. Calculate the standard deviation of the number
delivered when 8 local letters are mailed.
A) .85
B) .72
C) 2.68
D) 2.83
Answer: A
Explanation: σ =
=
=
= .85
Difficulty: 2 Medium
Topic: The Binomial Distribution
Learning Objective: 06-03 Use the binomial distribution to compute probabilities.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
349
Copyright 2019 © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior
written consent of McGraw-Hill Education.
135) The Post Office has established a record in a major midwestern city for delivering 90
percent of its local mail the next working day. When there are 8 local letters mailed, what is the
probability that the number delivered will be within 2 standard deviations of the mean?
A) .9950
B) .9619
C) .8131
D) .9996
Answer: B
Explanation:
P[σ = 7.2 ± 2(.85)] = P(σ = 7.2 ± 1.7) = P(5.5 ≤ x ≤8) = P(6 ≤ x ≤8)
= .4305 + .3826 + .1488 = .9619
Difficulty: 3 Hard
Topic: The Binomial Distribution
Learning Objective: 06-03 Use the binomial distribution to compute probabilities.
Bloom's: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
136) A car wash loses $30 on rainy days and makes $120 on days when it does not rain. If the
probability of rain is .15, calculate expected profit for the car wash.
A) $90
B) $76.50
C) $106.50
D) $97.50
Answer: D
Explanation: μx = (−30)(.15) + (120)(.85) = −4.50 + 102 = 97.50
Difficulty: 2 Medium
Topic: Discrete Probability Distributions
Learning Objective: 06-02 Find a discrete probability distribution and compute its mean and
standard deviation.
Bloom's: Apply
AACSB: Analytical Thinking
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137) An insurance company will insure a $75,000 particular make and model of car for its full
value against theft at a premium of $1,500 per year. Suppose that the probability that this
particular automobile make and model will be stolen is .0075. Calculate the expected net profit
for the insurance company.
A) $937.50
B) $551.25
C) $1488.75
D) $562.50
Answer: A
Explanation: μx = (−73,500)(.0075) + (1500)(.9925) = −551.25 + 1488.75 = 937.50
Difficulty: 3 Hard
Topic: Discrete Probability Distributions
Learning Objective: 06-02 Find a discrete probability distribution and compute its mean and
standard deviation.
Bloom's: Apply
AACSB: Analytical Thinking
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138) An insurance company will insure a $75,000 particular automobile make and model for its
full value against theft at a premium of $1500 per year. Suppose that the probability that this
particular make and model will be stolen is .0075. Find the premium that the insurance company
should charge if it wants its expected net profit to be $2000.
A) $1437.50
B) $2551.25
C) $2562.50
D) $2062.50
Answer: C
Explanation: 2000 = (x − 75,000)(.0075) + x(.9925) = .0075x − 562.5 + .9925x = 2562.5
Difficulty: 3 Hard
Topic: Discrete Probability Distributions
Learning Objective: 06-02 Find a discrete probability distribution and compute its mean and
standard deviation.
Bloom's: Apply
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139) A large disaster cleaning company estimates that 30 percent of the jobs it bids on are
finished within the bid time. Looking at a random sample of 8 jobs that it has contracted,
calculate the probability that exactly 4 of the jobs were not completed within the bid time.
A) .0081
B) .8059
C) .0580
D) .1361
Answer: D
Explanation: P(x = 4) = .1361
Difficulty: 2 Medium
Topic: The Binomial Distribution
Learning Objective: 06-03 Use the binomial distribution to compute probabilities.
Bloom's: Apply
AACSB: Analytical Thinking
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140) A large disaster cleaning company estimates that 30 percent of the jobs it bids on are
finished within the bid time. Looking at a random sample of 8 jobs that it has contracted,
calculate the mean number of jobs completed within the bid time.
A) 4.0
B) 2.4
C) 2.0
D) 5.6
Answer: B
Explanation: μx = np = 8(.3) = 2.4
Difficulty: 2 Medium
Topic: The Binomial Distribution
Learning Objective: 06-03 Use the binomial distribution to compute probabilities.
Bloom's: Apply
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141) A large disaster cleaning company estimates that 30 percent of the jobs it bids on are
finished within the bid time. Looking at a random sample of 8 jobs that it has contracted, find the
probability that x (number of jobs finished on time) is within one standard deviation of the mean.
A) .6867
B) .2541
C) .5506
D) .8844
Answer: B
Explanation:
μx = np = 8(0.3) = 2.4
σ=
=
= 1.3
2.4 ± 1.3 = (1.1, 3.7), which convert to (2, 3) for discrete probability
P(2 < x < 3) = 0.2541
Difficulty: 3 Hard
Topic: The Binomial Distribution
Learning Objective: 06-03 Use the binomial distribution to compute probabilities.
Bloom's: Apply
AACSB: Analytical Thinking
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142) Suppose that x has a hypergeometric distribution with N = 10, r = 5, and n = 3. Calculate
the mean of the distribution.
A) .500
B) .333
C) 1.500
D) 3.000
Answer: C
Explanation: n(r/N) = 3(5/10) = 1.5
Difficulty: 3 Hard
Topic: The Hypergeometric Distribution
Learning Objective: 06-05 Use the hypergeometric distribution to compute probabilities.
Bloom's: Apply
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143) Suppose that x has a hypergeometric distribution with N = 10, r = 5, and n = 3. Calculate
the standard deviation of the distribution.
A) .583
B) .764
C) 1.500
D) .778
Answer: B
Explanation:
σ2 = n(r/N)(1 − r/N)[(N − n)/(N − 1)] = 3(5/10)(.5)(7/9) = .583
σ=
= .764
Difficulty: 3 Hard
Topic: The Hypergeometric Distribution
Learning Objective: 06-05 Use the hypergeometric distribution to compute probabilities.
Bloom's: Apply
AACSB: Analytical Thinking
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144) If in a hypergeometric distribution r = 300, N = 600, and n = 30, estimate the binomial
probability of success.
A) .500
B) .333
C) .083
D) .250
Answer: A
Explanation: P = r/N = 300/600 = .500
Difficulty: 3 Hard
Topic: The Hypergeometric Distribution
Learning Objective: 06-05 Use the hypergeometric distribution to compute probabilities.
Bloom's: Apply
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145) Suppose you randomly select 3 DVDs from a production run of 10. Of the 10 DVDs, 9 are
expected to last a minimum of 3 years. What is the probability that all 3 of your DVDs will last
at least three years?
Answer: .7
P(x = 3) = (9C3 × 1C0)/10C3 = 84/120 = .7
Difficulty: 3 Hard
Topic: The Hypergeometric Distribution
Learning Objective: 06-05 Use the hypergeometric distribution to compute probabilities.
Bloom's: Apply
AACSB: Analytical Thinking
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146) Suppose you randomly select 3 DVDs from a production run of 10. Of the 10 DVDs, 9 are
expected to last a minimum of 3 years. What is the mean of the random variable x?
Answer: 2.7
Mean = n(r/N) = 3(9/10) = 2.7
Difficulty: 2 Medium
Topic: The Hypergeometric Distribution
Learning Objective: 06-05 Use the hypergeometric distribution to compute probabilities.
Bloom's: Apply
AACSB: Analytical Thinking
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147) Suppose you randomly select 3 DVDs from a production run of 10. Of the 10 DVDs, 9 are
expected to last a minimum of 3 years. What is the standard deviation of the random variable x?
Answer: .46
N = 10, n = 3, r = 9
S2 = n × (r/N) × [1 − (r/N)] × [(N − n)/(N − 1)] = (2.7 × .1 × .78) = .21
Therefore, standard deviation = s =
= .46
Difficulty: 2 Medium
Topic: The Hypergeometric Distribution
Learning Objective: 06-05 Use the hypergeometric distribution to compute probabilities.
Bloom's: Apply
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148) Suppose you randomly select 3 DVDs from a production run of 10. Of the 10 DVDs, 9 are
expected to last a minimum of 3 years. What values of x are within two standard deviations of
the mean?
Answer: 2 and 3
x = [2.7 ± 2(.46)] = (2.7 ± .92) = (1.78, 3.62)
Difficulty: 3 Hard
Topic: The Hypergeometric Distribution
Learning Objective: 06-05 Use the hypergeometric distribution to compute probabilities.
Bloom's: Apply
AACSB: Analytical Thinking
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149) The yearly proportional return for stock G = x, the yearly proportional return for stock H =
y, μx = .16, μy = .07, σx = .11, σy = .11, and σxy2 = .0321. Find the mean and standard deviation of
the portfolio return: P = .45x + .55y.
Answer: mean = .111; standard deviation = .148
μp = μ(.45x+.55y) = .45(.16) + .55(.07) = .111
σp = √[(.45)2(.111)2 + (.55)2(.111)2 + 2(.45)(.55)(.0321)] =
= .148
Difficulty: 3 Hard
Topic: Joint Distributions and the Covariance
Learning Objective: 06-06 Compute and understand the covariance between two random
variables.
Bloom's: Apply
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150) The yearly proportional return for stock G = x, the yearly proportional return for stock H =
y, μx = .16, μy = .07, σx = .11, σy = .11, and σxy2 = .0321. Find the mean and standard deviation of
the portfolio return: P = .5x + .5y.
Answer: mean = .115, standard deviation = .149
μp = μ(.5x+.5y) = .5(.16) + .5(.07) = .115
σp = √[(.5)2(.11)2 + (.5)2(.11)2 + 2(.5)(.5)(.0321)] =
= .149
Difficulty: 3 Hard
Topic: Joint Distributions and the Covariance
Learning Objective: 06-06 Compute and understand the covariance between two random
variables.
Bloom's: Apply
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