AP Statistics
Name:__________________________ Date:_____________ Period:___
SEMESTER 1 FINAL 2021/22
Multiple Choice: Each of the questions or incomplete statements is followed by five suggested answersor completions.
Select the one that best answers the question or completes the statement. Clearly mark your answers on the Scantron in pen
or pencil.
Leave this page blank!
1) A prom committee is formed of 10 seniors (6 of whom are male) and 6 juniors (1 of whom is male). A chairperson is
chosen at random. Find the probability that the chairperson will be a female or a senior.
a) 0.0625
b) 0.3125
c) 0.3750
d) 0.5625
e) 0.9375
2) Which of the following is not a discrete random variable:
a) The total distance travelled by a soccer ball during a game.
b) The number of students acing this test
c) The number of times Ms. Anderson fell on her last days on skis
d) The total number of finals given this week by the math department.
e) All of them are discrete.
3) Seventy smokers and 50 non-smokers with high blood pressure were subjects in an experiment to determine the
effectiveness of a new drug in lowering blood pressure. 35 of the 70 smokers and 25 of the 50 non-smokers were chosen
at random to receive the new drug. The remaining smokers and non-smokers received the placebo. The change in blood
pressure was measured for each subject. The design of this experiment is:
a) randomized block, blocked by smoking/non-smoking
b) randomized block, blocked by drug
c) randomized block, blocked by drug and smoking/non-smoking
d) completely randomized with one factor, drug
e) completely randomized with one factor, smoking/non-smoking
4) What is the equation of the regression line for the values in the table below?
X
Y
1
1
2
3
3
3
4
6
5
5
a) 𝑦 = 1.1 + 0.3𝑥
d) 𝑦 = 0.3 + 1.1𝑥
b) 𝑦 = 0.89𝑥 + 0.3
e) 𝑦 = 1.1 + 0.89𝑥
c) 𝑦 = 0.3 + 0.796𝑥
5) Which of these characteristics would be a qualitative/categorical variable?
a) barometric pressure level
b) time spent on SnapChat on weekends
c) average gas consumption for midsize pickup trucks
d) type of calculator used for this test
e) none of these
6) Cans of soft drinks cost $0.30 in a certain vending machine. The expected value and variance of the random variable X, the
number of cans sold per day, are given as:
E(X) = 125, and Var(X) = 50
The expected value and variance of the daily revenue (Y) is:
a) E(Y) = 37.5, Var(Y) = 50
b) E(Y) = 37.5, Var(Y) = 4.5
c) E(Y) = 37.5, Var(Y) = 15
d) E(Y) = 37.5, Var(Y) = 10
e) E(Y) = 125, Var(Y) = 4.5
7) The ‘mean’ is
a) a set of something (e.g., students, stars, elephants, etc.).
b) a specific type of graph.
c) a measure of variability
d) a measure of central tendency
e) the most common value of a data set
8) The ‘standard deviation’ is
a) a specific type of table.
b) a specific type of distribution of scores.
c) a z-score of 0.
d) a measure of variability.
e) a measure of central tendency.
9) A distribution that is skewed to the right has a mode of 56kg and a median of 65kg. Which of the following is
a possible value for the mean?
a) 50 kg
b) 56kg
c) 60kg
d) 65 kg
e) 72kg
10) The stemplot to the right shows ages of CEOs of a select group of corporations.
Which of the following is not a correct statement about this distribution?
a) The distribution is roughly bell-shaped.
b) The distribution is skewed left and right.
c) The center is around 60.
d) The spread is from 22 to 90.
e) There are no outliers.
11) The least square regression line was computed to be 𝑦 = −23.5 + 8.2𝑥 . The coefficient of correlation r is
a) positive
b) negative
c) either positive or negative
d) zero
e) cannot be determined
12) Which of the following statements regarding standard deviation is false?
a) Standard deviation is a measure of variability.
b) Standard deviation is the average distance data points lie away from the mean.
c) Standard deviation can only be calculated for normally distributed data sets.
d) Standard deviation is the square root of the variance.
e) None of the statements are false.
13) A distribution can have more than one
a) Mean
b) Interquartile range
c) Mode
d) Median
e) Standard deviation
14) Control groups are used in experiments in order to
a) Control the effects of outside variables on the outcome.
b) Control the subjects of a study to make sure everyone participates equally.
c) Ensure proper randomization.
d) Reduce variability in the results.
e) Avoid having to use a placebo.
15) Which of the following describes a situation in which it is reasonable to reach a cause-and-effect conclusion based on data
from a statistical study?
a) The study is based on a random sample from a population of interest.
b) The study is observational, and the sample is NOT a convenience sample.
c) The study is an experiment that uses random assignment to assign volunteers to treatments.
d) The study is observational, and the two samples are NOT convenience samples.
e) It is always reasonable to reach a cause-and-effect conclusion based on data from a statistical study.
16) A bank wishes to survey its customers. The decision is made to randomly pick 25 customers who just have banking
accounts, 25 customers who have only savings accounts and 25 customers who have both. This is an example of
a) simple random sampling
d) cluster sampling
b) systematic random sampling
e) convenience sampling
c) stratified random sampling
17) If P(L) = .4 and P(M) = .3, then the probability P(L and M) could equal any of the given answers except
a) 0
b) 0.1
c) 0.2
d) 0.3
e) 0.4
18) A local street contains 7 street lights. The probability that any one street light does not work is 0.30. Assuming
independence, what is the probability that at least one does not work?
a) 0.0002
b) 0.9998
c) 0.0824
d) 0.9176
e) 0.9563
19) The median is the measure of central tendency most commonly used for which types of distributions?
a) Normal distributions
d) Skewed distributions
b) Symmetric distributions
e) The median is never a good measure of
c) Uniform distributions
central tendency.
20) The weights of 10-year-old girls are known to be normally distributed with a mean of 70 pounds and a standard deviation
of 13 pounds. Find the percentage of 10-year-old girls with weights between 60 and 90 pounds.
a) – 0.7692
b) 0.2206
c) 0.7172
d) 0.9382
e) 1.5385
21) Suppose P(X) = .3 and P(Y|X) = .1. The P( X and Y) equals:
a) 0.01
b) 0.03
c) 0.1
d) 0.3
e) 0.4
22) Which of the following indicates that an association between x and y is positive?
a) A positive coefficient of determination
b) A positive standard deviation about the least-squares-regression line
c) A positive y-intercept of the least-squares-regression line
d) A positive x-intercept of the least-squares-regression line
e) A positive correlation coefficient
23) A psychologist studied the number of puzzles subjects were able to solve in a five-minute period while listening to
soothing music. Let X be the number of puzzles completed successfully by a subject. The psychologist found that X had the
following probability distribution.
Value of X
Probability
1
0.2
2
0.4
3
0.3
4
0.1
Referring to the information above, if three subjects solve puzzles for five minutes each and the numbers of puzzles
solved by the subjects are independent of each other, then the mean of the total number of puzzles solved by the three
subjects is
a) 1.8
b) 2.3
c) 2.5
d) 6.9
e) 7.5
24) There is a linear relationship between the number of chirps made by the striped ground cricket and the air temperature.
A least-squares fit of some data collected by a biologist gives the model 𝑦 = 25.2 + 3.3𝑥, where x is the number of chirps
per minute and 𝑦 is the estimated temperature in degrees Fahrenheit. What is the predicted temperature for a cricket
who chirps 15 chirps per minute?
a) 3.3°F
b) 74.7°F
c) 25.2°F
d) 49.5°F
e) 41.7°F
25) Which of these follows a geometric model?
a) The number of black cards present in a hand of 10 cards
b) The color of the cars in a parking lot
c) The number of people we survey until we find one who owns an iPod
d) The number of hits a baseball player gets in 6 times at bat
e) None of these events follow a geometric distribution
26) If removing an observation from a data set would have a marked change on the equation of the least-squares regression
line, the point is called
a) resistant.
b) a residual.
c) influential.
d) a response.
e) an outlier.
27) A number of students from Skyline High School were randomly selected and surveyed. They were asked if they had
attended the Winter Dance and if they had attended the talent show assembly last week. The results are shown below:
Talent Show
Dance
Attended
62
22
Attended
Not Attended
Not attended
19
97
Based on these data, the probability that a randomly selected student will have attended both events, given that they
attended at least one of them, is closest to which value?
a) 0.31
b) 0.60
c) 0.62
d) 0.74
e) 0.77
28) Let Z be a standard normal random variable. Which of the following probabilities is the smallest?
a) 𝑃(−2 < 𝑧 < −1)
d) 𝑃(𝑧 > −2)
b) 𝑃(0 < 𝑧 < 2)
e) 𝑃(𝑧 > 2)
c) 𝑃(𝑧 < 1)
29) Items produced by a manufacturing process are supposed to weigh 90 grams. However, the manufacturing process is
such that there is variability in the items produced and they do not all weigh exactly 90 grams. The distribution of
weights can be approximated by a normal distribution with a mean of 90 grams and a standard deviation of 1 gram.
Using the 68–95– 99.7 rule, what percentage of the items will either weigh less than 87 grams or more than 93 grams?
a) 0.3%
b) 3%
c) 6%
d) 94%
e) 99.7%
30) In a particular game, a fair die is tossed. If the number of spots showing is either 4 or 5 you win $1, if number of spots
showing is 6 you win $4, and if the number of spots showing is 1, 2, or 3 you win nothing. Let X be the amount that you
win when playing the game once. The expected value of X is
a) $0.00
b) $1.00
c) $2.50
d) $4.00
d) $6.00
31) The Skyline Student Parking lot sees its fair share of accidents. The table below shows the probability distribution of
witnessed accidents X per month.
X
0
1
2
3
4
5
P(X)
0.110
0.215
0.260
0.214
0.134
0.067
What is the probability that there are fewer than 3 accidents in any given month?
a) 0.201
b) 0.214
c) 0.585
32) If 𝑃(𝐴 ∩ 𝐵) = 0, then
a) A and B are independent
b) A and B are mutually exclusive
c) A and B are complements
33) The percentage of data falling at or below the upper quartile is
a) 25
b) 50
c) 75
d) 100
d) 0.799
e) none of these
d) A and B have the same probability
e) A and B are continuous
e) none of these
34) Through accounting procedures, it is known that about 10% of the employees in a store are stealing. The managers
would like to fire the thieves, but their only tool in distinguishing them from the honest employees is a lie detector test
that is only 90% accurate. That is, if an employee is a thief, he or she will fail the test with probability 0.9, and if an
employee is not a thief, he or she will pass the test with probability 0.9. If an employee fails the test, what is the
probability that he or she is a thief?
a) 90%
b) 75%
c) 66 2/3%
d) 50%
e) 10%
35) Consider the continuous random variable X = the weight in pounds of a randomly newborn baby born in the United
States during 2006. Suppose that X can be modeled with a normal distribution with mean µ = 7.57 and standard
deviation σ = 1.06. If the mean were µ = 7.27 instead, how would that change the graph of the pdf of X?
a) The graph would be shifted to the left.
b) The graph would be shifted to the right.
c) The graph would become more skewed.
d) The graph would stay exactly the same
e) We cannot comment since we do not know the new standard deviation.
36) The following Venn diagram uses the following definition: D = people who exercise on weekdays. W = people who
exercise on the weekends. What does the shaded region represent?
D
W
a)
b)
c)
d)
e)
people who don’t exercise on weekdays
people who exercise on weekdays
people who exercise on weekends only
people who exercise on weekdays only
people who never exercise
37) A least-squares regression line is fitted to a set of data. If one of the data points has a positive residual, then
a) the point must lie near the right edge of the scatterplot.
b) the slope of the least-squares regression line must be positive.
c) the correlation between the values of the response and explanatory variables must be positive.
d) the point must lie above the least-squares regression line.
e) all of the above.
38) A school guidance counselor examines the number of extracurricular activities of students and their grade point average.
The guidance counselor says, “The evidence indicates that the correlation between the number of extracurricular
activities a student participates in and his or her grade point average is close to zero.” A correct interpretation of this
statement would be that
a) Students with good grades tend to be students that are not involved in many activities, and vice versa.
b) Students involved in many extracurricular activities are just as likely to get good grades as bad grades. The same
is true for students involved in few extracurricular activities.
c) Active students tend to be students with poor grades, and vice versa.
d) As a student becomes more involved in extracurricular activities, there will be a change in their grades.
e) Involvement in many extracurricular activities and good grades go hand in hand.
39) A researcher is interested in determining if one can predict the score a student gets on a statistics exam from the
amount of time the student spends studying for the exam. In this study, the explanatory variable is
a) the amount of time spent studying for the
c) the score on the exam.
exam.
d) the fact that this is a statistics exam.
b) the students taking the exam.
e) the researcher.
40) The distribution of actual weights of 8.0-ounce chocolate bars produced by a certain machine is normal with a mean of
8.1 ounces and a standard deviation of 0.1 ounces. The expected weight of a 2-pack of said chocolate bars selling for
$1.59 is
a) 8.1 oz
b) 8.2 oz
c) 11.5 oz
d) 12.9 oz
e) 16.2 oz
41) In a class of 100 students, the grades on a statistics test are summarized in the following frequency table.
Grade
The median grade is in which of the following intervals?
91-100
a) 61–70.
81-90
b) 71–80.
71-80
c) 81–90.
61-70
d) 91–100.
e) Since the number of individual values is not known, the median cannot be determined.
Frequency
11
31
42
16
42) Consider the following probability histogram for a discrete random variable X. This probability histogram corresponds to
which of the following probability distributions for X?
a) .
b) .
d) .
c) .
e) None of the above
43) Suppose there are three balls in a box. On one of the balls is the number 1, on another is the number 2, and on the third
is the number 3. You select two balls at random and without replacement from the box and note the two numbers
observed. The sample space S consists of the three equally likely outcomes {(1, 2), (1, 3), (2, 3)}. Let X be the sum of the
numbers on the two balls selected. The variance of X is
a) 1/3
b) 2/3
c) 0.816
d) 1
e) 4
44) In the following table, what value for n results in a table showing perfect independence?
a) 10
A
Ac
B
20
50
Bc
30
n
b) 40
c) 60
d) 75
e) 100
45) The boxplot below represents the time required, in minutes, for 452 students to finish the final exam in a statistics
course at a large university. How many students took less than 85 minutes to finish the exam?
a) 85
b) 113
c) 226
d) 339
e) 452
46) For a normally distributed random variable x with  = 0 and  = 1, the population interquartile range is closest to which
of the following values?
a) 0.5
b) 1.28
c) 1.349
d) 1.645
e) 1.96
47) The data summarized in this 2-way chart reflect the results of asking 50 students in a public school and 50 students in a
private school what musical instrument they had learned to play. In cases where students had learned to play more than
one instrument, they were instructed to choose the instrument they had played for the longest amount of time. Which
kind of graphical representation would best compare these data?
a)
b)
c)
d)
e)
Side-by-side pie charts
Two histograms
Side-by-side stemplots
Side-by-side boxplots
Any of these charts would adequately compare these data.
48) The pie chart displays the details of Audrey's investment portfolio. The portfolio's value is $766,400. The common stocks
are composed of 4 different types of stocks: Blue Chip Stocks: 42%, Small Cap Stocks: 23%, Foreign Stocks: 20%, and
Penny Stocks: 15%.
Based on the pie chart above, what percent of the entire portfolio consists of Small Cap Stocks?
a) 5%
b) 9%
c) 11%
d) 20%
e) 23%
49) Cucumbers grown on a certain farm have weights that are normally distributed with a standard deviation of 2 ounces.
What is the approximate mean weight of the cucumbers if 85% of the cucumbers weigh less than 16 ounces?
a) 13.9 oz.
b) 14.3 oz.
c) 14 oz.
d) 14.9 oz.
e) 15.7 oz.
50) What does it mean to get a z-score of –2.00 on this exam?
a) It means you missed 2 questions on this exam.
b) It means you missed twice as many questions on this exam as the average student.
c) It means that your grade was two standard deviations below the mean on this exam.
d) It means that your grade was 2 points lower than the average on this exam.
e) It means your IQ could be about a 2 points lower than normal.