m
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
1. A group of men and women were polled about whether they go to the gym regularly. The joint and marginal
relative frequencies corresponding to the results are shown in the two-way table.
What is the value of x?
a. 1
b. 0.5
____
2. A group of men and women were polled about whether they go to the gym regularly. The joint and marginal
relative frequencies corresponding to the results are shown in the two-way table.
What is the value of y?
a. 1
b. 0.5
____
c. 0.2
d. 0.1
c. 0.2
d. 0.1
3. A contractor working alone can pour cement for a sidewalk in 2 hours. It takes his assistant 3.5 hours to do it
alone. How long would it take if the contractor and the assistant work together?
Which table shows the joint and relative frequencies?
a.
b.
c.
d.
____
4. Joyce asked 50 randomly-selected students at her school whether they have one or more brothers or sisters.
The table shows the results of Joyce’s poll.
Make a table of the joint and marginal relative frequencies. Express percentages in decimal form.
a.
b.
c.
d.
____
5. In recent years, the three most popular car colors in the United States have been black, silver, and white.
Suppose a poll of 40 randomly-selected car buyers gave the following results. The table shows how men’s
and women’s preferences differed in the poll.
Make a table of the joint and marginal relative frequencies. Express percentages in decimal form.
a.
b.
c.
d.
____
6. A poll of 100 senior citizens in a retirement community asked about the types of electronic communication
they used.The table shows the joint and marginal frequencies from the poll results.
If you are given that one of the people polled uses text messaging, what is the probability that the person is
also using e-mail? Express your answer as a decimal. If necessary, round your answer to the nearest
hundredth.
a.
b.
c.
d.
____
7. At a small high school, there are 80 girls in the senior class. Some of them play basketball, some play soccer,
some play both, and some play neither. The table shows the joint and marginal frequencies for the senior
girls.
If you know that a girl plays soccer, what is the probability that she also plays basketball? Express your
answer as a decimal. If necessary, round your answer to the nearest hundredth.
a.
b.
c.
d.
____
0.65
0.61
0.8
0.13
0.08
0.23
0.43
0.3
8. A study compared the on-time performance for three bus companies. A table with the joint and marginal
frequencies of the results is shown.
Determine which company has the best on-time performance. Explain how to identify the company that
performed best.
a. Red Dog Transit has the best on-time performance; Divide the joint relative frequency of
on-time arrival by the marginal relative frequency to find the best performance.
b. Cross-Country Bus has the best on-time performance; Identify the greatest joint relative
frequency of on-time arrivals to find the best performance.
c. Express Way Lines has the best on-time performance; Divide the joint relative frequency
of on-time arrival by the marginal relative frequency to find the best performance.
d. Cross-Country Bus has the best on-time performance; Divide the joint relative frequency
of on-time arrival by the marginal relative frequency to find the best performance.
____
9. Suppose the United States House of Representatives voted to pass a bill. The voting results are shown in the
two-way table. Does the table show any difference in voting patterns between Democrats and Republicans?
a. There are no differences in voting patterns.
b. More Republicans than Democrats voted “no”, so Republicans were more likely to oppose
the bill than Democrats were.
c. Both Democrats and Republicans tended to favor the bill.
d. Republicans tended to vote “yes” on the bill. Democrats were slightly more likely to vote
“no” than to vote “yes”.
____ 10. At a wedding reception, the guests have a choice of chicken or steak for dinner. Do more people prefer
chicken or steak? Do more people under 40 prefer chicken or steak?
a.
b.
c.
d.
More people prefer chicken. However, more people under 40 prefer steak.
More people prefer chicken. Also, more people under 40 prefer chicken.
More people prefer steak. Also, more people under 40 prefer steak.
More people prefer steak. However, more people under 40 prefer chicken.
____ 11. At State College, 458 juniors and seniors are taking a performing arts course. 217 sing in the chorus, 74 are in
theater, and the rest are in dance. No one takes more than one performing arts course. There are 87 juniors
taking chorus, 33 seniors taking theater, and a total of 263 seniors taking a performing arts course. Make a
two-way frequency table for the data.
a.
b.
c.
d.
Short Answer
1. The table shows the number of students playing spring sports at a local school. How many girls play a spring
sport?
2. The pets at an animal shelter were either surrendered by their owners or caught as strays. One year, the shelter
took in a total of 1457 animals. Of these, 482 were dogs, 916 were cats, and the rest were other types of
animals. There were 178 stray dogs, 456 surrendered cats, and a total of 653 stray animals. Make a two-way
table for the data.
3. On a given day at school, 417 students, 202 of them are boys, bought either juice, milk, or water to drink at
lunchtime. Ninety-seven students bought juice and 190 bought milk. Fifty-six girls bought water and 92 boys
bought milk. Make a two-way frequency table to display the data.
4. A school has two campuses. The two-way frequency table shows the number of students and teachers at each
campus.
Find the ratio of students to teachers at East campus Round your answer tot he nearest hundredth.
Find the ratio of students to teachers at West campus. Round your answer to the nearest hundredth.
Which campus has a lower student to teacher ratio?
5. Marcia and Marvin are playing with miniature cars and trucks. Together they have 89 toy vehicles. Marvin
has 54 vehicles, of which 21 were trucks. There are 32 total toy trucks. Make a two-way frequency table to
display the data.
6. A total of 1125 tickets were sold to the spring musical which was performed on Friday, Saturday, and
Sunday. Two hundred adult tickets were sold for Friday’s performance and 225 adult tickets for Saturday’s
performance. Over the three days, 526 student tickets were sold, 164 of them for Saturday. Three hundredfifty tickets were sold for Friday’s performance. Make a two-way frequency table for the data.
7. A survey about favorite spring vacation destinations asked 163 students to choose between Florida, Colorado,
and Texas. Eighty-one of these students were girls. Fifty-seven students chose Florida and 35 chose Colorado.
Twenty-eight of the boys chose Texas while 35 of the boys chose Florida. Make a two-way frequency table to
display the data.
8. The two-way frequency table shows all of the grades in Mr. Tobin’s two geometry classes. If period 5 were to
have the same percent of A’s as the period 2 class, how many more students would need to get an A in the
period 5 class?
Essay
1. The two-way frequency table shows the favorite part of watching a school football game for people in two
age groups.
Find how many more people surveyed prefer the football game to the half-time show. Explain how you found
your answer.
If a person between the ages of 30 and 39 is chosen at random, which of these three aspects of the game is he
or she least likely to prefer? Explain your reasoning.
2. 120 randomly-selected high school students were asked to choose which of the four following varsity sports-baseball, football, basketball, or lacrosse--they liked best.
Of the males, 14 chose baseball, 16 chose football, 18 chose basketball, and 14 chose lacrosse.
Of the females, 12 chose baseball, 16 chose football, 14 chose basketball, and 16 chose lacrosse.
Part A: Make a two-way frequency table from the data.
Part B: Make a table of the joint and marginal relative frequencies. Round to the nearest hundredth where
appropriate.
Part C: In the table of joint and marginal relative frequencies, what do the values represent? Give examples
from the table to illustrate your answer.
3. The table shows the joint relative frequencies for data on the books checked out from a school library last
week.
Hardcover
Paperback
Nonfiction
0.215
0.206
Fiction
0.217
0.362
Part A: Find the marginal relative frequencies for the data. Round to the nearest thousandth where
appropriate. How can you check that these numbers are correct?
Part B: Is it possible to determine from the table the total number of books that were checked out? Why or
why not?
Part C: Based on these data, is a nonfiction book more likely to be a hardcover book or a paperback book?
Explain your work, and round your answer to the nearest hundredth.
m
Answer Section
MULTIPLE CHOICE
1. ANS:
DOK:
2. ANS:
DOK:
3. ANS:
DOK:
4. ANS:
OBJ:
NAT:
TOP:
DOK:
5. ANS:
OBJ:
NAT:
TOP:
DOK:
6. ANS:
OBJ:
NAT:
TOP:
DOK:
7. ANS:
NAT:
TOP:
DOK:
8. ANS:
OBJ:
NAT:
TOP:
DOK:
9. ANS:
TOP:
DOK:
10. ANS:
TOP:
DOK:
11. ANS:
TOP:
DOK:
C
PTS: 1
NAT: NT.CCSS.MTH.10.9-12.S.ID.5
DOK 1
D
PTS: 1
NAT: NT.CCSS.MTH.10.9-12.S.ID.5
DOK 1
D
PTS: 1
NAT: NT.CCSS.MTH.10.9-12.S.ID.5
DOK 2
C
PTS: 1
REF: 906d9aa8-6ab2-11e0-9c90-001185f0d2ea
Finding Joint and Marginal Relative Frequencies
NT.CCSS.MTH.10.9-12.S.CP.4 | NT.CCSS.MTH.10.9-12.S.ID.5
Two-Way Tables
KEY: two-way tables
DOK 2
D
PTS: 1
REF: 906ffd03-6ab2-11e0-9c90-001185f0d2ea
Finding Joint and Marginal Relative Frequencies
NT.CCSS.MTH.10.9-12.S.CP.4 | NT.CCSS.MTH.10.9-12.S.ID.5
Two-Way Tables
KEY: two-way tables
DOK 2
B
PTS: 1
REF: 90702413-6ab2-11e0-9c90-001185f0d2ea
Using Conditional Relative Frequency to Find Probability
NT.CCSS.MTH.10.9-12.S.CP.4 | NT.CCSS.MTH.10.9-12.S.CP.5 | NT.CCSS.MTH.10.9-12.S.ID.5
Two-Way Tables
KEY: two-way tables
DOK 3
B
PTS: 1
REF: 90725f5e-6ab2-11e0-9c90-001185f0d2ea
NT.CCSS.MTH.10.9-12.S.CP.4 | NT.CCSS.MTH.10.9-12.S.CP.5 | NT.CCSS.MTH.10.9-12.S.ID.5
Two-Way Tables
KEY: two-way tables
DOK 3
C
PTS: 1
REF: 9072866e-6ab2-11e0-9c90-001185f0d2ea
Comparing Conditional Probabilities
NT.CCSS.MTH.10.9-12.S.CP.4 | NT.CCSS.MTH.10.9-12.S.ID.5
Two-Way Tables
KEY: two-way tables
DOK 3
D
PTS: 1
NAT: NT.CCSS.MTH.10.9-12.S.ID.5
Analyze Data
KEY: two-way table
DOK 1
B
PTS: 1
NAT: NT.CCSS.MTH.10.9-12.S.ID.5
Analyze Data
KEY: two-way table
DOK 1
A
PTS: 1
NAT: NT.CCSS.MTH.10.9-12.S.ID.5
Analyze Data
KEY: two-way table
DOK 1
SHORT ANSWER
1. ANS:
86
PTS: 1
NAT: NT.CCSS.MTH.10.9-12.S.ID.5
KEY: two-way table
DOK: DOK 1
2. ANS:
TOP: Analyze Data
PTS: 1
NAT: NT.CCSS.MTH.10.9-12.S.ID.5
KEY: two-way table
DOK: DOK 1
3. ANS:
TOP: Analyze Data
PTS: 1
NAT: NT.CCSS.MTH.10.9-12.S.ID.5
4. ANS:
14.68; 17.36; The ratio is lower at East campus.
DOK: DOK 2
PTS: 1
5. ANS:
NAT: NT.CCSS.MTH.10.9-12.S.ID.5
DOK: DOK 2
PTS: 1
6. ANS:
NAT: NT.CCSS.MTH.10.9-12.S.ID.5
DOK: DOK 2
PTS: 1
7. ANS:
NAT: NT.CCSS.MTH.10.9-12.S.ID.5
DOK: DOK 2
PTS: 1
8. ANS:
1 student
NAT: NT.CCSS.MTH.10.9-12.S.ID.5
DOK: DOK 2
PTS: 1
NAT: NT.CCSS.MTH.10.9-12.S.ID.5
DOK: DOK 2
ESSAY
1. ANS:
Seventeen more people prefer the game to the half-time show.
He or she is least likely to prefer socializing with friends since only 8 chose socializing with friends compared
to 23 and 36 who chose the half-time show and the game.
PTS: 1
2. ANS:
Part A:
Male
Female
NAT: NT.CCSS.MTH.10.9-12.S.ID.5
Baseball
14
12
Football
16
16
DOK: DOK 2
Basketball
18
14
Lacrosse
14
16
Part B:
Male
Female
Total
Baseball
0.12
0.1
0.22
Football
0.13
0.13
0.26
Basketball
0.15
0.12
0.27
Lacrosse
0.12
0.13
0.25
Total
0.52
0.48
1
Part C: The values that are not in the Total row or column are the joint relative frequencies. They represent
the proportion of the total number of students surveyed who fall into that category. For example, of all
students surveyed, 0.15 of them were males who chose basketball as their favorite sport. The values in the
Total row and column are the marginal relative frequencies. They represent the proportion of the total number
of students surveyed who fall into that row or column. For example, of all students surveyed, 0.52 of them
were male and 0.22 of them chose baseball as their favorite sport.
PTS: 1
NAT: NT.CCSS.MTH.10.9-12.S.ID.5
KEY: two-way table
DOK: DOK 2
3. ANS:
Part A: hardcover: 0.432; paperback: 0.568; nonfiction: 0.421; fiction: 0.579
The sum of the marginal relative frequencies of hardcover and paperback should be equal to 1, and the sum of
the marginal relative frequencies of nonfiction and fiction should also be equal to 1.
Part B: No; the values in the table represent percentages of the total number of books checked out; from this
information alone, you cannot determine the actual number of books.
Part C: 0.421 of the books were nonfiction; of this portion, 0.215 were hardcover. So, if a book is nonfiction,
the probability that it is also a hardcover is
PTS: 1
DOK: DOK 3
.
NAT: NT.CCSS.MTH.10.9-12.S.ID.5
KEY: two-way table