Question ID 85939da5
Assessment Test Domain Skill Difficulty
SAT Math Problem-Solving Inference from
and Data Analysis sample statistics
and margin of error
ID: 85939da5
Does not talk
Texting Talks on cell on cell phone
behavior phone daily daily Total
Light 110 146 256
Medium 139 164 303
Heavy 166 74 240
Total 415 384 799
In a study of cell phone use, 799 randomly selected US teens were asked how
often they talked on a cell phone and about their texting behavior. The data are
summarized in the table above. Based on the data from the study, an estimate of
the percent of US teens who are heavy texters is 30% and the associated margin
of error is 3%. Which of the following is a correct statement based on the given
margin of error?
A. Approximately 3% of the teens in the study who are classified as heavy texters are not really heavy texters.
B. It is not possible that the percent of all US teens who are heavy texters is less than 27%.
C. The percent of all US teens who are heavy texters is 33%.
D. It is doubtful that the percent of all US teens who are heavy texters is 35%.
ID: 85939da5 Answer
Correct Answer: D
Rationale
Choice D is correct. The given margin of error of 3% indicates that the actual percent of all US teens who are
heavy texters is likely within 3% of the estimate of 30%, or between 27% and 33%. Therefore, it is unlikely, or
doubtful, that the percent of all US teens who are heavy texters would be 35%.
Choice A is incorrect. The margin of error doesn’t provide any information about the accuracy of reporting in the
study. Choice B is incorrect. Based on the estimate and given margin of error, it is unlikely that the percent of all
US teens who are heavy texters would be less than 27%, but it is possible. Choice C is incorrect. While the percent
of all US teens who are heavy texters is likely between 27% and 33%, any value within this interval is equally
likely. We can’t be certain that the value is exactly 33%.
Question Difficulty: Hard
,Question ID 3c8fdc40
Assessment Test Domain Skill Difficulty
SAT Math Problem-Solving Ratios, rates,
and Data Analysis proportional
relationships, and
units
ID: 3c8fdc40
A printer produces posters at a constant rate of posters per minute. At what rate, in posters per hour, does the printer
produce the posters?
ID: 3c8fdc40 Answer
Correct Answer: 2520
Rationale
The correct answer is 2,520. There are 60 minutes in one hour. At a rate of 42 posters per minute, the number of
42 posters 60 minutes
posters produced in one hour can be determined by , which is 2,520 posters per hour.
1 minute 1 hour
Question Difficulty: Easy
,Question ID e29586d5
Assessment Test Domain Skill Difficulty
SAT Math Problem-Solving Probability and
and Data Analysis conditional
probability
ID: e29586d5
Number of Contestants by Score and Day
5 4 3 2 1 0
out out out out out out Total
of 5 of 5 of 5 of 5 of 5 of 5
Day
2 3 4 6 2 3 20
1
Day
2 3 5 5 4 1 20
2
Day
3 3 4 5 3 2 20
3
Total 7 9 13 16 9 6 60
The same 20 contestants, on each of 3 days, answered 5 questions in order to win a prize. Each contestant received 1
point for each correct answer. The number of contestants receiving a given score on each day is shown in the table
above.
No contestant received the same score on two different days. If a contestant is
selected at random, what is the probability that the selected contestant received
a score of 5 on Day 2 or Day 3, given that the contestant received a score of 5 on
one of the three days?
ID: e29586d5 Answer
Rationale
The correct answer is . It is given that no contestant received the same score on two different days, so each of
the contestants who received a score of 5 is represented in the “5 out of 5” column of the table exactly once.
Therefore, the probability of selecting a contestant who received a score of 5 on Day 2 or Day 3, given that the
contestant received a score of 5 on one of the three days, is found by dividing the total number of contestants
who received a score of 5 on Day 2 or Day 3 by the total number of contestants who received a score of
5, which is given in the table as 7. So the probability is . Note that 5/7, .7142, .7143, and 0.714 are examples of
ways to enter a correct answer.
Question Difficulty: Hard
, Question ID eccbf957
Assessment Test Domain Skill Difficulty
SAT Math Problem-Solving Probability and
and Data Analysis conditional
probability
ID: eccbf957
Each face of a fair -sided die is labeled with a number from through , with a different number appearing on each
face. If the die is rolled one time, what is the probability of rolling a ?
A.
B.
C.
D.
ID: eccbf957 Answer
Correct Answer: A
Rationale
Choice A is correct. The total number of possible outcomes for rolling a fair 14-sided die is 14. The number of
possible outcomes for rolling a 2 is 1. The probability of rolling a 2 is the number of possible outcomes for rolling
1
a 2 divided by the total number of possible outcomes, or 14
.
Choice B is incorrect. This is the probability of rolling a number no greater than 2.
Choice C is incorrect. This is the probability of rolling a number greater than 2.
Choice D is incorrect. This is the probability of rolling a number other than 2.
Question Difficulty: Easy
Assessment Test Domain Skill Difficulty
SAT Math Problem-Solving Inference from
and Data Analysis sample statistics
and margin of error
ID: 85939da5
Does not talk
Texting Talks on cell on cell phone
behavior phone daily daily Total
Light 110 146 256
Medium 139 164 303
Heavy 166 74 240
Total 415 384 799
In a study of cell phone use, 799 randomly selected US teens were asked how
often they talked on a cell phone and about their texting behavior. The data are
summarized in the table above. Based on the data from the study, an estimate of
the percent of US teens who are heavy texters is 30% and the associated margin
of error is 3%. Which of the following is a correct statement based on the given
margin of error?
A. Approximately 3% of the teens in the study who are classified as heavy texters are not really heavy texters.
B. It is not possible that the percent of all US teens who are heavy texters is less than 27%.
C. The percent of all US teens who are heavy texters is 33%.
D. It is doubtful that the percent of all US teens who are heavy texters is 35%.
ID: 85939da5 Answer
Correct Answer: D
Rationale
Choice D is correct. The given margin of error of 3% indicates that the actual percent of all US teens who are
heavy texters is likely within 3% of the estimate of 30%, or between 27% and 33%. Therefore, it is unlikely, or
doubtful, that the percent of all US teens who are heavy texters would be 35%.
Choice A is incorrect. The margin of error doesn’t provide any information about the accuracy of reporting in the
study. Choice B is incorrect. Based on the estimate and given margin of error, it is unlikely that the percent of all
US teens who are heavy texters would be less than 27%, but it is possible. Choice C is incorrect. While the percent
of all US teens who are heavy texters is likely between 27% and 33%, any value within this interval is equally
likely. We can’t be certain that the value is exactly 33%.
Question Difficulty: Hard
,Question ID 3c8fdc40
Assessment Test Domain Skill Difficulty
SAT Math Problem-Solving Ratios, rates,
and Data Analysis proportional
relationships, and
units
ID: 3c8fdc40
A printer produces posters at a constant rate of posters per minute. At what rate, in posters per hour, does the printer
produce the posters?
ID: 3c8fdc40 Answer
Correct Answer: 2520
Rationale
The correct answer is 2,520. There are 60 minutes in one hour. At a rate of 42 posters per minute, the number of
42 posters 60 minutes
posters produced in one hour can be determined by , which is 2,520 posters per hour.
1 minute 1 hour
Question Difficulty: Easy
,Question ID e29586d5
Assessment Test Domain Skill Difficulty
SAT Math Problem-Solving Probability and
and Data Analysis conditional
probability
ID: e29586d5
Number of Contestants by Score and Day
5 4 3 2 1 0
out out out out out out Total
of 5 of 5 of 5 of 5 of 5 of 5
Day
2 3 4 6 2 3 20
1
Day
2 3 5 5 4 1 20
2
Day
3 3 4 5 3 2 20
3
Total 7 9 13 16 9 6 60
The same 20 contestants, on each of 3 days, answered 5 questions in order to win a prize. Each contestant received 1
point for each correct answer. The number of contestants receiving a given score on each day is shown in the table
above.
No contestant received the same score on two different days. If a contestant is
selected at random, what is the probability that the selected contestant received
a score of 5 on Day 2 or Day 3, given that the contestant received a score of 5 on
one of the three days?
ID: e29586d5 Answer
Rationale
The correct answer is . It is given that no contestant received the same score on two different days, so each of
the contestants who received a score of 5 is represented in the “5 out of 5” column of the table exactly once.
Therefore, the probability of selecting a contestant who received a score of 5 on Day 2 or Day 3, given that the
contestant received a score of 5 on one of the three days, is found by dividing the total number of contestants
who received a score of 5 on Day 2 or Day 3 by the total number of contestants who received a score of
5, which is given in the table as 7. So the probability is . Note that 5/7, .7142, .7143, and 0.714 are examples of
ways to enter a correct answer.
Question Difficulty: Hard
, Question ID eccbf957
Assessment Test Domain Skill Difficulty
SAT Math Problem-Solving Probability and
and Data Analysis conditional
probability
ID: eccbf957
Each face of a fair -sided die is labeled with a number from through , with a different number appearing on each
face. If the die is rolled one time, what is the probability of rolling a ?
A.
B.
C.
D.
ID: eccbf957 Answer
Correct Answer: A
Rationale
Choice A is correct. The total number of possible outcomes for rolling a fair 14-sided die is 14. The number of
possible outcomes for rolling a 2 is 1. The probability of rolling a 2 is the number of possible outcomes for rolling
1
a 2 divided by the total number of possible outcomes, or 14
.
Choice B is incorrect. This is the probability of rolling a number no greater than 2.
Choice C is incorrect. This is the probability of rolling a number greater than 2.
Choice D is incorrect. This is the probability of rolling a number other than 2.
Question Difficulty: Easy
