Name:
Chapters 1-6 Homework Worksheets
Chapter 2
1. Consider the following part of a data set:
List the variables in the data set. Indicate whether each variable is treated as categorical or quantitative
in this data set. If the variable is quantitative, state the units.
For problems 2 & 3: Describe the W's (Who, What, When, Where, How, Why), if the information is given.
If the information is not given, state that it is not specified. Also, list the variables. Indicate whether
each variable is categorical or quantitative. If the variable is quantitative, tell the units.
2. The State Education Department requires local school districts to keep these records on all students:
age, race or ethnicity, days absent, current grade level, standardized test scores in reading and math, and
any disabilities or special education needs.
3. One of the reasons that the Monitoring the Future (MTF) project was started was "to study changes in
the beliefs, attitudes, and behavior of young people in the United States." Data are collected from 8th,
10th, and 12th graders each year. To get a representative nationwide sample, surveys are given to a
randomly selected group of students. In Spring 2004, students were asked about alcohol, illegal drug, and
cigarette use. Describe the W's, if the information is given. If the information is not given, state that it
is not specified.
1
AP Statistics – Classwork Chapter 3
Smoking and Education
200 adults shopping at a supermarket were asked about the highest level of education they had
completed and whether or not they smoke cigarettes. Results are summarized in the table.
Smoker
Non-Smoker
1. Discuss the W’s.
High School
32
61
2 yr college
5
17
4+ yr college
13
72
Total
50
150
2. Identify the variables.
3. a) What percent of the shoppers were smokers with only high school educations? ______
b) What percent of the shoppers with only high school educations were smokers? ______
c) What percent of the smokers had only high school educations? ______
4. Create a segmented bar graph comparing education level
among smokers and non-smokers. Label your graph clearly
5. Do these data suggest there is an association between smoking and education level? Give statistical
evidence to support your conclusion.
6. Follow-up question: Does this indicate that students who start smoking while in high school tend to give
up the habit if they complete college? Explain.
7. Consider the following pie charts of a subset of the data below:
Do the pie charts above indicate that milk consumption by
young girls is independent of the nationwide survey year? Explain.
2
Total
93
22
85
200
Has the percentage of young girls drinking milk changed over time? The following table is consistent with
the results from "Beverage Choices of Young Females: Changes and Impact on Nutrient Intakes" (Shanthy
A. Bowman, Journal of the American Dietetic Association, 102(9), pp. 1234-1239):
Nationwide Food Survey Years
1987-1988
1989-1991
1994-1996
Total
Drinks Fluid
Yes
354
502
366
1222
Milk
No
226
335
366
927
Total
580
837
732
2149
8. Identify the variables and tell whether each is categorical or quantitative.
9. Which of the W’s are unknown for these data?
10. Find the following:
a. What percent of the young girls reported that they drink milk?
b. What percent of the young girls were in the 1989-1991 survey?
c. What percent of the young girls who reported that they drink milk were in the 1989-1991 survey?
d. What percent of the young girls in 1989-1991 reported that they drink milk?
11. What is the marginal distribution of milk consumption?
12. Write a sentence or two about the conditional relative frequency of the people who said that they did
not drink fluid milk.
13. Do you think that milk consumption by young girls is independent of the nationwide survey year? Use
statistics to justify your reasoning.
Chapter 3 Extra Practice- Multiple Choice
1. Which one of the following variables is categorical?
a.
b.
c.
d.
e.
the type of text book
the daily high temperature
the fraction of material in a statistics class understood by a student
the number of classes taken by a college freshman
the weight of babies born at a large hospital
2. Which of the following is the appropriate calculation to find the number of degrees in each portion of a pie graph?
a.
relative frequency
d.
360
3
relative frequency
360
total
b.
frequency
360
total
e. none are correct
c. frequenc y 360
Chapter 3 Free Response Practice
3. (2011A #2) The table below shows the political party registration by gender of all 500 registered
voters in Franklin Township.
Party Registration- Franklin Township
Party W
Party X
Party Y
Total
Female
60
120
120
300
Male
28
124
48
200
Total
88
244
168
500
(a) Given that a randomly selected registered voter is a male, what is the probability that he is
registered for Party Y?
(b) Among the registered voters of Franklin Township, are the events “is a male” and “is registered for
Party Y” independent? Justify your answer based on probabilities calculated from the table above.
(c) One way to display the data in the table is to use a segmented bar graph. The following segmented bar
graph, constructed from the data in the party registration–Franklin Township table, shows partyregistration distributions for males and females in Franklin Township.
In Lawrence Township, the proportions of all registered voters for Parties W, X, and Y are the same as
for Franklin Township, and party registration is independent of gender. Complete the graph below to show
the distributions of party registration by gender in Lawrence Township.
4
3. 2010 #5
An advertising agency in a large city is conducting a survey of adults to investigate whether there is an
association between highest level of educational achievement and primary source for news. The company
takes a random sample of 2,500 adults in the city. The results are shown in the table below.
Highest Level of Educational Achievement
Primary Source for Not a H.S. Grad
H.S. Grad, but not
College Grad
Total
News
a College Grad
Newspapers
49
205
188
442
Local Television
90
170
75
335
Cable Television
113
496
147
756
Internet
41
401
245
687
None
77
165
38
280
Total
370
1,437
693
2,500
(a) If an adult is to be selected at random from this sample, what is the probability that the selected
adult is a college graduate or obtains news primarily from the internet?
(b) If an adult who is a college graduate is to be selected at random from this sample, what is the
probability that the selected adult obtains news primarily from the internet?
(c) When selecting an adult at random from the sample of 2,500 adults, are the events “is a college
graduate” and “obtains news primarily from the internet” independent? Justify your answer.
Chapter 4 Worksheet
1. The frequency table below shows the heights (in inches) of 130 members of a choir.
Height 60
61
62
63
64
65
66
67
68
69
70
71
72
73
Count
2
6
9
7
5
20
18
7
12
5
11
8
9
4
a. Find the median and IQR.
b. Find the mean and standard deviation
c. Display these data with a histogram.
d. Write a few sentences describing the distribution.
5
74
2
75
4
76
1
2. The following is a breakdown of win-loss records for SEC teams during the 2010 football season:
East
West
South Carolina
9-5
Auburn
14-0
Florida
8-5
LSU
11-2
Georgia
6-7
Arkansas
10-3
Tennessee
6-7
Alabama
10-3
Kentucky
6-7
Mississippi State
9-4
Vanderbilt
2-10
Ole Miss
4-8
a. Make a 5-number summary for the win totals for SEC teams.
Minimum:
Q1:
Median:
Q3:
Maximum:
b. Find the Interquartile Range (IQR) for the win totals.
c. Find the mean and standard deviation for win totals.
d. Display the data with the following pictures:
i. Histogram
ii. Stem and Leaf Plot
iii. Dotplot
e. Describe the center of the data. (What’s the best measure? Mean/Median?)
f. Describe anything unusual in the data. (Any outliers/gaps?)
g. Describe the spread of the data. (Range, IQR or standard deviation?)
h. Describe the shape of the data. (Is it symmetric? skewed? Unimodal/bimodal/multimodal/uniform?)
6
3. The following table shows Electoral College votes by state. You also need to include Washington D.C.
with your data, they have 3 electoral votes.
State
AL
AK
AZ
AR
CA
CO
CN
DE
FL
GA
#
9
3
10
6
55
9
7
3
27
15
State
HI
ID
IL
IN
IA
KS
KY
LA
ME
MD
#
4
4
21
11
7
6
8
9
4
10
State
MA
MI
MN
MS
MO
MT
NE
NV
NH
NJ
#
12
17
10
6
11
3
5
5
4
15
State
NM
NY
NC
ND
OH
OK
OR
PA
RI
SC
#
5
31
15
3
20
7
7
21
4
8
State
SD
TN
TX
UT
VT
VA
WA
WV
WI
WY
#
3
11
34
5
3
13
11
5
10
3
a. Make a 5-number summary for the electoral votes for each state (including DC).
Minimum:
Q1:
Median:
Q3:
Maximum:
b. Find the Interquartile Range (IQR) for the Electoral College votes.
c. Find the mean and standard deviation for the Electoral College votes.
d. Display the data with the following pictures:
i. Histogram
ii. Stem and Leaf Plot
e. Describe the center of the data. (What’s the best measure? Mean/Median?)
f. Describe anything unusual in the data. (Any outliers/gaps?)
g. Describe the spread of the data. (Range, IQR or standard deviation?)
h. Describe the shape of the data. (Is it symmetric? skewed? Unimodal/bimodal/multimodal/uniform?)
7
4. Listed below are the final regular season standings for the 2010 NFL season.
NFC Teams
Win-Loss Record AFC Teams
Atlanta
13-3
New England
Win-Loss
Record
14-2
Chicago
11-5
Pittsburgh
12-4
New Orleans
11-5
Baltimore
12-4
Philadelphia
10-6
NY Jets
11-5
Green Bay
10-6
Indianapolis
10-6
NY Giants
10-6
Kansas City
10-6
Tampa Bay
Seattle
10-6
7-9
San Diego
Jacksonville
9-7
8-8
St. Louis
7-9
Oakland
8-8
Minnesota
6-10
Miami
7-9
Detroit
6-10
Houston
6-10
Dallas
6-10
Tennessee
6-10
Washington
6-10
Cleveland
5-11
San Francisco
6-10
Cincinnati
4-12
Arizona
5-11
Denver
4-12
Carolina
2-14
Buffalo
4-12
a. Sketch a histogram for the wins.
b. Find the mean and standard deviation for the win
totals
c. Is it appropriate to use the mean and
d. Describe the associations of win totals.
standard deviations to summarize the data?
5. Mr. Hubbard collected data from his students about how many times that “tweet” a day on their
Twitter accounts. Out of all his students, the highest number of tweets per day was 16. Today, Mr.
Hubbard got a new student in his Algebra 1 class. Mr. Hubbard asked the student how many times they
tweeted in a day and the student said 25. If Mr. Hubbard were to include the new student’s total into his
data, would it cause the following summary statistics to increase, decrease, or stay about the same.
a. Mean:
______________________________________
b. Median:
______________________________________
c. Range:
______________________________________
d. IQR:
______________________________________
e. standard deviation: _____________________________________
8
Chapter 4 Multiple Choice
6. The figure above shows a cumulative relative frequency
histogram of 40 scores on a test given in an AP Statistics class.
Which of the following conclusions can be made from the graph?
(A) There is greater variability in the lower 20 test scores than in the higher 20 test scores.
(B) The median test score is less than 50.
(C) Sixty percent of the students had test scores above 80.
(D) If the passing score is 70, most students did not pass the test.
(E) The horizontal nature of the graph for the test scores of 60 and below indicates that those scores
occurred most frequently.
Chapter 4 Free Response Review
7. (2007B- #1) The Better Business Council of a large city has concluded that students in the city’s
schools are not learning enough about economics to function in the modern world. These findings were
based on test results from a random sample of 20 12 th grade students who completed a 46-question
multiple-choice test on basic economics concepts. The data set below shows the number of questions that
each of the 20 students answered correctly:
12
16
18
17
18
33
41
44
38
35
19
36
19
13
43
8
16
14
10
9
a. Display these data in a stemplot
b. Use your stemplot from part (a) to describe the main features of this score distribution.
c. Why would it be misleading to report only a measure of center for this score distribution?
9
8. (2005B- #1) The graph below displays the scores of 32 students on a recent exam. Scores on this exam
ranged from 64 to 95 points
6
**
6
**
7
***
7
****
8
****
8
******
9
*******
9
****
a. Describe the shape of this distribution
b. In order to motivate her students, the instructor of the class wants to report that, overall, the class’s
performance on the exam was high. Which summary statistic, the mean or the median, should the
instructor use to report that overall exam performance was high? Explain.
c. The midrange is defined as
max imum  min imum
. Compute this value using the data above. Is the
2
midrange considered a measure of center or a measure of spread? Explain.
Chapter 5
AP Statistics – Classwork Chapter 5
1. Here are the weekly payrolls for two imaginary restaurants,
Mooseburgers and McTofu.
a. Find the 5-number summaries.
Statistic
M-burgers McTofu
Min
Q1
Median
Q3
Max
b. Create parallel boxplots. Label your graph clearly.
10
Mooseburgers
Al $123
Boris $136
Connie $144
Dwight $150
Ernie $110
Francois $131
Gloria $140
Horace $160
Issac $120
Juan $130
McTofu
Ken $110
Latisha $115
Maria $130
Nate $100
Otto $120
Pablo $146
Quentin $117
Sally $360
Ted $132
Uta $107
c. Write a few sentences comparing the distributions.
d. Which restaurant pays the higher average salary? ________________________
e. Why is the mean salary misleading?
f. At which restaurant would you rather work? Give a sound statistical justification for your
decision.
2. As of 2010, here is a list of top earners in the field of reality TV and Late Night/Talk Syndication with
the salaries made per year:
Oprah Winfrey
$315 million
Judge Judy Sheindlin
$45 million
David Letterman
(The Late Show)
$28 million
Jay Leno
(The Tonight Show)
$25 million
Ryan Seacrest
(American Idol)
$15 million
Conan O'Brien
(The Conan O'Brien Show)
$10 million
Ellen DeGeneres
(The Ellen DeGeneres Show)
$8 million
Jimmy Kimmel
(Jimmy Kimmel Live)
$6 million
Chelsea Handler
(Chelsea Lately)
$3.5 million
George Lopez
(Lopez Tonight)
$3.5 million
Joel McHale
(The Soup)
$2 million
Piers Morgan
(America's Got Talent)
$2 million
a. Generate a 5-number summary for the data.
Min
Q1
Median
Q3
Max
b. Would you expect the mean salary for money made per year to be higher or lower than the median?
Explain.
c. Were any of the salaries outliers? Show (by hand) how to find an outlier.
HINT: Use Q1 – 1.5(IQR) and Q3 + 1.5(IQR) to establish your range.
11
Here are a list of the top 10 earners in news:
Matt Lauer
(Today)
$16 million +
Katie Couric
(CBS)
$15 million
Brian Williams
(NBC)
$12.5 million
Diane Sawyer
(ABC)
$12 million
Meredith Vieira
(Today)
$11 million
Bill O'Reilly
(Fox News)
$10 million
George Stephanopoulos
(ABC)
$8 million
Keith Olbermann
(MSNBC)
$7 million
Shepard Smith
(Fox News)
$7 million
Wolf Blitzer
(CNN)
$3 million
d. Make a parallel box-and-whisker plot for the reality/Late Night TV people and the news people:
e. Which group has the highest median pay and what is the amount?
f. Which group has the largest IQR and what is it?
g. Which group generally gets paid more? Explain.
h. What would you use to describe center and spread for the reality/Late Night TV group? What would
you use for the news group?
i. Write a few sentences to describe the parallel box and whisker plots above.
j. What could you do to the reality/Late Night TV group to make the data more symmetric?
12
3. The five-number summary for midterm scores (number of points; the maximum possible score was 50
points) from an intro stats class is:
a. Would you expect the mean midterm score of all students who took the midterm to be higher or lower
than the median? Explain.
b. Based on the five-number summary, are any of the midterm scores outliers? Explain.
4. The side-by-side boxplots show the cumulative college GPAs for sophomores, juniors, and seniors taking
an intro stats course in Autumn 2003.
a. Which class (sophomore, junior, or senior) had the lowest cumulative college GPA?
What is the approximate value of that GPA?
b. Which class had the highest median GPA, and what is that GPA?
c. Which class had the largest range for GPA, and what is it?
d. Which class had the most symmetric set of GPAs?
The most skewed set of GPAs?
e. Which class generally had the highest GPA? Explain.
Chapter 5 Multiple Choice Review
5. The boxplots shown above summarize two data sets, I and II. Based on the boxplots, which of the
following statements about these two data sets CANNOT be justified?
(A) The range of data set I is equal to the range of data set II.
(B) The interquartile range of data set I is equal to the interquartile range of data set II.
(C) The median of data set I is less than the median of data set II.
(D) Data set I and data set II have the same number of data points.
(E) About 75% of the values in data set II are greater than or equal to about 50% of the values in data
set I.
13
Chapter 5 Free Response Review
6. (2008A- #1)To determine the amount of sugar in a typical serving of breakfast cereal, a student
randomly selected 60 boxes of different types of cereal from the shelves of a large grocery store.
The student noticed that the side panels of some of the cereal boxes showed sugar content based on onecup servings, while others showed sugar content based on three-quarter-cup servings. Many of the cereal
boxes with side panels that showed three-quarter-cup servings were ones that appealed to young children,
and the student wondered whether there might be some difference in the sugar content of the cereals
that showed different-size servings on their side panels. To investigate the question, the data were
separated into two groups. One group consisted of 29 cereals that showed one-cup serving sizes; the
other group consisted of 31 cereals that showed three-quarter-cup serving sizes. The boxplots shown
below display sugar content (in grams) per serving of the cereals for each of the two serving sizes.
(a) Write a few sentences to compare the distributions of sugar content per serving for the two serving
sizes ofcereals.
After analyzing the boxplots on the preceding page, the student decided that instead of a comparison of
sugar content per recommended serving, it might be more appropriate to compare sugar content for
equal-size servings. To compare the amount of sugar in serving sizes of one cup each, the amount of sugar
in each of the cereals showing three-quarter-cup servings on their side panels was multiplied by
4
. The
3
bottom boxplot shown below displays sugar content (in grams) per cup for those cereals that showed a
serving size of three-quarter-cup on their side panels.
(b) What new information about sugar content do the boxplots above provide?
(c) Based on the boxplots shown above on this page, how would you expect the mean amounts of sugar per
cup to compare for the different recommended serving sizes? Explain.
14
7. (2010B- #1) As a part of the United States Department of Agriculture’s Super Dump cleanup efforts
in the early 1990s, various sites in the country were targeted for cleanup. Three of the targeted sites—
River X, River Y, and River Z—had become contaminated with pesticides because they were located near
abandoned pesticide dump sites. Measurements of the concentration of aldrin (a commonly used pesticide)
were taken at twenty randomly selected locations in each river near the dump sites.
The boxplots shown below display the five-number summaries for the concentrations, in parts per million
(ppm) of aldrin, for the twenty locations that were sampled in each of the three rivers.
(a) Compare the distributions of the concentration of aldrin among the three rivers.
(b) The twenty concentrations of aldrin for River X are given below.
3.4 4.0 5.6 3.7 8.0 5.5 5.3 4.2 4.3 7.3 8.6 5.1 8.7 4.6 7.5 5.3 8.2 4.7 4.8 4.6
Construct a stemplot that displays the concentrations of aldrin for River X.
(c) Describe a characteristic of the distribution of aldrin concentrations in River X that can be seen in
the stemplot but cannot be seen in the boxplot.
8. (2009B- #1) As gasoline prices have increased in recent years, many drivers have expressed concern
about the taxes they pay on gasoline for their cars. In the United States, gasoline taxes are imposed by
both the federal government and by individual states. The boxplot below shows the distribution of the
state gasoline taxes, in cents per gallon, for all 50 states on January 1, 2006.
15
(a) Based on the boxplot, what are the approximate values of the median and the interquartile range of
the distribution of state gasoline taxes, in cents per gallon? Mark and label the boxplot to indicate how
you found the approximated values.
(b) The federal tax imposed on gasoline was 18.4 cents per gallon at the time the state taxes were in
effect. The federal gasoline tax was added to the state gasoline tax for each state to create a new
distribution of combined gasoline taxes. What are approximate values, in cents per gallon, of the median
and interquartile range of the new distribution of combined gasoline taxes? Justify your answer.
9. (2011B- #1) Records are kept by each state in the United States on the number of pupils enrolled in
public schools and the number of teachers employed by public schools for each school year. From these
records, the ratio of the number of pupils to the number of teachers (P-T ratio) can be calculated for
each state. The histograms below show the P-T ratio for every state during the 2001–2002 school year.
The histogram on the left displays the ratios for the 24 states that are west of the Mississippi River, and
the histogram on the right displays the ratios for the 26 states that are east of the Mississippi River.
(a) Describe how you would use the histograms to estimate the median P-T ratio for each group (west and
east) of states. Then use this procedure to estimate the median of the west group and the median of the
east group.
(b) Write a few sentences comparing the distributions of P-T ratios for states in the two groups (west
and east) during the 2001–2002 school year.
(c) Using your answers in parts (a) and (b), explain how you think the mean P-T ratio during the
2001–2002 school year will compare for the two groups (west and east).
16
Chapter 6 Worksheet
1. The distribution of ACT scores are normal with the national average ACT score (mean) being 21.0 with a
standard deviation of 4.7.
a. Draw and Label the Normal Model (68-95-99.7) for the distribution of ACT scores.
b. What is the score of students who score in the 50 th percentile?
c. What is the score of the top 2.5% of ACT test takers?
d. What is the range of scores of the students scoring the middle 95 th percent?
e. What is the Interquartile Range of ACT scores nationwide?
f. What percent of students score between a 19 and 25 on the ACT?
g. For the NCAA Clearinghouse, a student with a high school GPA of 2.5 needs to score around a 17 on the
ACT to be eligible for Division 1 athletics. What percent of people taking the ACT each year would NOT
be eligible? Would you consider a score of 17 to be unusually low?
h. A student with a 3.0 GPA would need to score around a 12 on the ACT. What percent of people taking
the ACT each year would NOT be eligible? Would you consider a score of 12 to be unusually low?
i. What is a range of scores that you consider to be unusually small? What is a range of scores you
consider to be universally big?
j. The average ACT score for the state of Arkansas was 19.9 for the year 2011. What percentile does
Arkansas rate in relation to the national average? Would you say that the gap is significant?
17
k. The average ACT score for Prairie Grove High School was 22.3 in 2009. What percentile does Prairie
Grove rank in relation to the national average? Would you say that the gap is significant?
l. Arkansas Tech will give a full scholarship for students who achieve a 3.25 GPA and a 26 on the ACT.
What percent of students nationwide would have an ACT high enough to be eligible for this scholarship?
Would you consider this to be an unusually high score?
m. For most academic scholarships from the University of Arkansas, an ACT score of 30 minimum is
required among other things. What percent of students nationwide score a 30 or above on the ACT?
Would you consider this to be an unusually high score?
n. A perfect score on the ACT is a 36. What percent of students score a 36 on the ACT? Would you
consider this to be an unusually high score?
o. What is the range for which virtually all scores occur?
p. Explain what it would mean if the standard deviation of the ACT test got smaller?
q. Explain what it would mean if the standard deviation of the ACT test got bigger?
2. There is a rough formula used to convert ACT scores to SAT scores:
SAT = 40 X ACT + 150
Calculate the SAT equivalent for the following summary statistics:
a. Mean
b. Q1
c. Q3
d. IQR
e. Standard Deviation
f. Max (ACT score of 36)
18
g. What would be more unusual, an ACT score of 12 or an ACT score of 30?
h. What would be more unusual, an ACT score of 26 or an SAT score of 1000?
i. What would be more impressive, an ACT score of 30 or an SAT score of 1,300?
j. Say the SAT wanted to make sure that virtually everyone achieved a score of 500. If the mean SAT
score stayed the same, how would the standard deviation need to be adjusted to make this happen?
3) The army reports that the distribution of head circumference among soldiers is approximately normal
with mean 22.8 inches and standard deviation of 1.1 inches.
a) What is the probability that a randomly selected soldier’s head will have a circumference that is
greater than 23.5 inches?
b) What is the probability that a randomly selected soldier’s head will have a circumference that is
between 20 than 23 inches?
c) How many inches in circumference would a soldier’s head be if it were at the 40 th percentile?
d) Helmets are mass-produced for all except the smallest 5% and the largest 5%. Soldiers in the smallest
and largest 5% get custom-made helmets. What head sizes get custom-made helmets?
4) Here are the prices (in cents per pound) of bananas from 15 markets surveyed by the U. S.
Department of Agriculture. Are banana prices normally distributed? Justify your answer.
51
52
45
42
50
48
53
52
50
49
52
48
43
46
45
5) A gasoline tank for a certain car is designed to hold 15 gallons of gas. Suppose the capacity of gas
tanks are normally distributed with mean of 15 gallons and standard deviation of 0.1 gallon.
a) What is the probability that a randomly selected tank will hold at most 14.8 gallons?
b) What is the probability that a randomly selected tank will hold between 14.7 and 15.1
gallons?
19
c) How many gallons would a tank hold if it were at the 3 rd quartile of this distribution?
d) If two gas tanks are independently selected, what is the probability that both tanks hold at most 15
gallons?
6) Suppose that for the population of students at a particular university, the time required to
complete a standardized exam is normally distributed with mean 45 minutes and standard deviation
5 minutes.
a) If 50 minutes is allowed for the exam, what proportion of students at this university would be
unable to finish in the allotted time?
b) What proportion of students at this university would finish the exam in more than 38 minutes, but less
than 48 minutes?
c) How much time should be allowed for the exam if we wanted 90% of the students taking the test to be
able to finish in the allotted time?
d) How much time is required for the fastest 25% of all students to complete the exam?
Chapter 6 Multiple Choice Review
7. Lauren is enrolled in a very large college calculus class. On the first exam, the class mean was 75 and
the standard deviation was 10. On the second exam, the class mean was 70 and the standard deviation
was 15. Lauren scored 85 on both exams. Assuming the scores on each exam were approximately normally
distributed, on which exam did Lauren score better relative to the rest of the class?
(A) She scored much better on the first exam.
(B) She scored much better on the second exam.
(C) She scored about equally well on both exams.
(D) It is impossible to tell because the class size is not given.
(E) It is impossible to tell because the correlation between the two sets of exam scores is not given.
8. Suppose that the distribution of a set of scores has a mean of 47 and a standard deviation of 14. If 4
is added to each score, what will be the mean and the standard deviation of the distribution of new
scores?
Mean
Standard Deviation
(A)
51
14
(B)
51
18
(C)
47
14
(D)
47
16
(E)
47
18
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9. The lengths of individual shellfish in a population of 10,000 shellfish are approximately normally
distributed with mean 10 centimeters and standard deviation 0.2 centimeter. Which of the following is
the shortest interval that contains approximately 4,000 shellfish lengths?
(A) 0 cm to 9.949 cm
(B) 9.744 cm to 10 cm
(C) 9.744 cm to 10.256 cm
(D) 9.895 cm to 10.105 cm
(E) 9.9280 cm to 10.080 cm
10. In a carnival game, a person can win a prize by guessing which one of 5 identical boxes contains the
prize. After each guess, if the prize has been won, a new prize is randomly placed in one of the
5 boxes. If the prize has not been won, then the prize is again randomly placed in one of the 5 boxes.
If a person makes 4 guesses, what is the probability that the person wins a prize exactly 2 times?
2!
5!
(0.2)2
(B)
(0.8)2
(A)
(C) 2(0.2)(0.8)
(D) (0.2)2(0.8)2
(E)
 4
2
2
   0.2   0.8 
 2
Chapter 6- AP Free Response Review
11. (2009A- #2) A tire manufacturer designed a new tread pattern for its all-weather tires. Repeated
tests were conducted on cars of approximately the same weight traveling at 60 miles per hour. The tests
showed that the new tread pattern enables the cars to stop completely in an average distance of 125 feet
with a standard deviation of 6.5 feet and that the stopping distances are approximately normally
distributed.
(a) What is the 70th percentile of the distribution of stopping distances?
(b) What is the probability that at least 2 cars out of 5 randomly selected cars in the study will stop in a
distance that is greater than the distance calculated in part (a) ?
(c) What is the probability that a randomly selected sample of 5 cars in the study will have a mean
stopping distance of at least 130 feet?
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12. (2011A #1) A professional sports team evaluates potential players for a certain position based on two
main characteristics, speed and strength.
(a) Speed is measured by the time required to run a distance of 40 yards, with smaller times indicating
more desirable (faster) speeds. From previous speed data for all players in this position, the times to run
40 yards have a mean of 4.60 seconds and a standard deviation of 0.15 seconds, with a minimum time of
4.40 seconds, as shown in the table below.
Mean
Standard Deviation
Minimum
Time to run 40 yards
4.60 seconds
0.15 seconds
4.40 seconds
Based on the relationship between the mean, standard deviation, and minimum time, is it reasonable to
believe that the distribution of 40-yard running times is approximately normal? Explain.
(b) Strength is measured by the amount of weight lifted, with more weight indicating more desirable
(greater) strength. From previous strength data for all players in this position, the amount of weight
lifted has a mean of 310 pounds and a standard deviation of 25 pounds, as shown in the table below.
Mean
Standard Deviation
Amount of Weight Lifted
310 pounds
25 pounds
Calculate and interpret the z-score for a player in this position who can lift a weight of 370 pounds.
(c) The characteristics of speed and strength are considered to be of equal importance to the team in
selecting a player for the position. Based on the information about the means and standard deviations of
the speed and strength data for all players and the measurements listed in the table below for Players A
and B, which player should the team select if the team can only select one of the two players? Justify
your answer.
Player A
Player B
Time to run 40 yards
4.42 seconds
4.57 seconds
Amount of Weight Lifted
370 pounds
375 pounds
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