ALGEBRA II
WITH
TRIGONOMETRY: FINAL EXAM REVIEW 2015
UNIT STAT: STATISTICS
DUE DATE: _______________
STAT 1: Designing a Study
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Survey, Experiment and Observational Study
Bias in Surveys and Experiments
Shape, Center and Spread
Five Number Summary
Skewed Left, Skewed Right, Symmetrically Distributed
STAT 2: Normal Distribution
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Normal Distributions and The Empirical Rule
Standard Deviation
Z scores
Z SCORE
z=
x -m
s
=
x-x
s
PROBLEM SET
1) A sports drink company gives out free samples of their new sports drink at the mall.
They record the number of teens versus the number of adults that take the sample. Does
this situation represent a survey, an experiment, or an observational study?
2) At the Democratic National Convention, people are asked if they are going to vote for
a Democratic or Republican candidate for
president. Is this a biased or unbiased
Who Do You Support for President?
survey? If biased, explain your reasoning.
Democratic
Republican
Other
Candidate
Candidate
Candidate
94%
MD/PH/CR/RS 6-15
3%
3%
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ALGEBRA II
WITH
TRIGONOMETRY: FINAL EXAM REVIEW 2015
3) Students in a biology class found the average number of minutes that they each spent
participating in extracurricular activities each day.
2nd Period
122, 0, 95, 45, 122, 35, 0, 165, 0, 45, 30, 30, 125, 0, 60, 95, 122, 0, 165, 30, 45, 25
6th Period
60, 95, 30, 122, 65, 60, 90, 45, 0, 60, 90, 65, 0, 35, 45, 0, 122, 35, 0, 60, 90
a. Describe the shape of each distribution.
b. Compare the distributions using either the means and standard deviations or the fivenumber summaries. Justify your choice.
4) Jack's scores in Chemistry this semester were rather inconsistent: 100, 85, 55, 95,
75, 100. For this sample, how many scores are within one standard deviation of the
mean?
5) The time it takes a bicycle courier to deliver a parcel to his farthest customer is
normally distributed with a mean of 38.6 minutes and a standard deviation of 4.7 minutes.
a. About what percent of the courier’s trips to this customer take between 35 and 40
minutes?
b. About what percent of the courier’s trips to this customer take between 40 and 45
minutes?
c. About what percent of the courier’s trips to this customer take less than 30 minutes?
6) Professor Dunphy has 184 students in his college mathematics lecture class. The
scores on the midterm exam are normally distributed with a mean of 72.3 and a standard
deviation of 8.9. How many students in the class can be expected to receive a score
between 82 and 90? Express answer to the nearest student.
7) A shoe manufacturer collected data regarding men's shoe sizes and found that the
distribution of sizes exactly fits the normal curve. If the mean shoe size is 11 and the
standard deviation is 1.5, find:
a. the probability that a man's shoe size is greater than or equal to 11.
b. the probability that a man's shoe size is greater than or equal to 12.5
MD/PH/CR/RS 6-15
Page 2 of 3
ALGEBRA II
WITH
TRIGONOMETRY: FINAL EXAM REVIEW 2015
8) The daily July surface temperature of a lake at a resort has a mean of 82˚ and a
standard deviation of 4.2˚. If you prefer to swim when the temperature is at least 80˚,
about what percent of the days does the temperature meet your preference?
9) A normal distribution has a mean of 287 and a standard deviation of 65.
a) What range of values represents the middle 68% of the data?
b) What percent of data will be more than 417?
c) What range of values represents the low 0.15% of the data?
10) The salaries at a manufacturing plant are normally distributed with a mean of
$59,500 and a standard deviation of $13,360. How much must an employee earn to be in
the top 16% of paid employees?
11) The mile times for students at Ridgemont High School are normally distributed with a
mean of 510 seconds and a standard deviation of 90 seconds. What time must a student
run the mile in if the student wants to finish in the top 2.5% of times?
12) The amount of mustard dispensed from a machine at Hot Diggity Dog is normally
distributed with a mean of 0.9 ounce and a standard deviation of 0.1 ounce. If the
machine is used 500 times, approximately how many times will it be expected to dispense
1 or more ounces of mustard.
13) Convert the following test scores to z-scores and then decide which is the student’s
strongest and weakest area of performance.
Test
Score
Mean
English
Science
History
87
90
75
80
92
55
MD/PH/CR/RS 6-15
Standard
Deviation
5
16
18
Z-Score
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