# Expert Answers

Question 1 of 40

In the first series of rolls of a die, the number of odd numbers exceeded the number of even numbers by 5. In the second series of rolls of the same die, the number of odd numbers exceeded the number of even numbers by 11. Determine which series is closer to the 50/50 ratio of odd/even expected of a fairly rolled die.

A. The second series is closer because the difference between odd and even numbers is greater than the difference for the first series.

B. The first series is closer because the difference between odd and even numbers is less than the difference for the second series.

C. Since 1/2 1/5 1/11, the first series is closer.

D. The series closer to the theoretical 50/50 cannot be determined unless the total number of rolls for both series is given

Question 2 of 40

A class consists of 50 women and 82 men. If a student is randomly

selected, what is the probability that the student is a woman?

A. 32/132

B. 27/66

C. 50/132

D. 82/132

Question 3 of 40

Suppose you have an extremely unfair die: The probability of a 6 is 3/8, and the probability of each other number is 1/8. If you toss the die 32 times, how many twos do you expect to see?

A. 2 B. 4 C. 3 D. 5

Question 4 of 40 If a person is randomly selected, find the probability that his or her birthday is not in May. Ignore leap years. There are 365 days in a year. Express your answer as a fraction.

A. 335/365 B. 334/365 C. 336/365 D. 30/365

Question 5 of 40

The data set represents the income levels of the members of a country club. Estimate the probability that a randomly selected member earns at least $98,000. 112,000 126,000 90,000 133,000 94,000 112,000 98,000 82,000 147,000 182,000 86,000 105,000 140,000 94,000 126,000 119,000 98,000 154,000 78,000 119,000

A. 0.4 B. 0.6 C. 0.66 D. 0.7

Question 6 of 40

If you flip a coin three times, the possible outcomes are HHH, HHT, HTH, HTT, THH, THT, TTH, TTT. What is the probability of getting at least one head?

A. 4/9 B. 5/6 C. 7/8 D. 5/8

Question 7 of 40

A study of 600 college students taking Statistics 101 revealed that 54 students received the grade of A. Typically 10% of the class gets an A. The difference between this group of students and the expected value is not significant at the 0.05 level. What does this mean in this case?

A. The probability that the difference occurred due to chance is less than 0.05.

B. The probability of getting an A is 10% and only 9% got an A in this study. The difference is less than 5% so it is not significant.

C. There is not enough information to make any conclusion.

D. The probability that the difference occurred due to chance is more than 0.05.

Question 8 of 40 On a multiple choice test, each question has 6 possible answers. If you make a random guess on the first question, what is the probability that you are correct?

A. 1/5 B. 1/6 C. 1/4 D. 2/5

Question 9 of 40

Suppose you buy 1 ticket for $1 out of a lottery of 1000 tickets where the prize for the one winning ticket is to be $500. What is your expected value? A. $0.00 B. −$0.40 C. −$1.00 D. −$0.50

Question 10 of 40

If you flip a coin three times, the possible outcomes are HHH, HHT, HTH, HTT, THH, THT, TTH, TTT. What is the probability of getting at least two tails?

A. 1/2 B. 2/3 C. 3/4 D. 4/9

Question 11 of 40 A study of students taking Statistics 101 was done. Four hundred students who studied for more than 10 hours averaged a B. Two hundred students who studied for less than 10 hours averaged a C. This difference was significant at the 0.01 level. What does this mean?

A. The probability that the difference was due to chance alone is greater than 0.01.

B. There is less than a 0.01 chance that the first group’s grades were better by chance alone.

C. The improvement was due to the fact that more people studied.

D. There is not enough information to make any conclusion.

Question 12 of 40 Of 1308 people who came into a blood bank to give blood, 314 people had high blood pressure. Estimate the probability that the next person who comes in to give blood will have high blood pressure (to 3 decimal places). A. 0.250 B. 0.490 C. 0.240 D. 0.160

Question 13 of 40 Suppose you pay $1.00 to roll a fair die with the understanding that you will get back $3.00 for rolling a 5 or a 2, nothing otherwise. What is your expected value?

A. $1.00 B. $0.00 C. $3.00 D. −$1.00

Question 14 of 40 A 28-year-old man pays $125 for a one-year life insurance policy with coverage of $140,000. If the probability that he will live through the year is 0.9994, to the nearest dollar, what is the man’s expected value for the insurance policy?

A. $139,916 B. −$41 C. $84 D. −$124

Question 15 of 40 Based on meteorological records, the probability that it will snow in a certain town on January 1st is 0.413. Find the probability that in a given year it will not snow on January 1st in that town. A. 0.345 B. 0.425 C. 0.587 D. 0.592

Question 16 of 40 Suppose you have an extremely unfair coin: the probability of a head is 1/5, and the probability of a tail is 4/5. If you toss the coin 40 times, how many heads do you expect to see?

A. 8 B. 6 C. 5 D. 4

Question 17 of 40 The probability that Luis will pass his statistics test is 0.94. Find the probability that he will fail his statistics test. A. 0.02 B. 0.05 C. 0.94 D. 0.06

Question 18 of 40 Suppose you have an extremely unfair coin: the probability of a head is 1/3 and the probability of a tail is 2/3. If you toss the coin 72 times, how many heads do you expect to see?

A. 12 B. 22 C. 24 D. 26

Question 19 of 40

A committee of three people is to be formed. The three people will be selected from a list of five possible committee members. A simple random sample of three people is taken, without replacement, from the group of five people. Using the letters A, B, C, D, E to represent the five people, list the possible samples of size three and use your list to determine the probability that B is included in the sample. (Hint: There are 10 possible samples.) A. 0.6 B. 0.4 C. 0.7 D. 0.8

Question 20 of 40 A die with 12 sides is rolled. What is the probability of rolling a number less than 11? Is this the same as rolling a total less than 11 with two six-sided dice? Explain. A. 2/6 B. 3/6

C. 4/6 D. 5/6

Question 21 of 40 A researcher wishes to estimate the proportion of college students who cheat on exams. A poll of 490 college students showed that 33% of them had, or intended to, cheat on examinations. Find the margin of error for the 95% confidence interval.

A. 0.0432 B. 0.0434 C. 0.0425 D. 0.0427

Question 23 of 40 A random sample of 30 households was selected from a particular neighborhood. The number of cars for each household is shown below. Estimate the mean number of cars per household for the population of households in this neighborhood. Give the 95% confidence interval.

2 0 1 2 3 2 1 0 1 4

1 3 2 0 1 1 2 3 1 2

1 0 2 3 0 2 2 1 0 2

A. 1.14 to 1.88 B. 1.12 to 1.88 C. 1.12 to 1.98 D. 1.14 to 1.98

Question 24 of 40 In a poll of 400 voters in a certain state, 61% said that they opposed a voter ID bill that might hinder some legitimate voters from voting. The margin of error in the poll was reported as 4 percentage points (with a 95% degree of confidence). Which statement is correct?

A. The reported margin of error is consistent with the sample size. B. There is not enough information to determine whether the margin of error is consistent with the sample size. C. The sample size is too small to achieve the stated margin of error. D. For the given sample size, the margin of error should be smaller than stated.

Question 27 of 40 30% of the fifth grade students in a large school district read below grade level. The distribution of sample proportions of samples of 100 students from this population is normal with a mean of 0.30 and a standard deviation of 0.045. Suppose that you select a sample of 100 fifth grade students from this district and find that the proportion that reads below grade level in the sample is 0.36. What is the probability that a second sample would be selected with a proportion less than 0.36?

A. 0.8932 B. 0.8920 C. 0.9032 D. 0.9048

Question 31 of 40 A population proportion is to be estimated. Estimate the minimum sample size needed to achieve a margin of error E = 0.01with a 95% degree of confidence.

A. 7,000 B. 8,000 C. 9,000 D. 10,000

Question 32 of 40 Eleven female college students are selected at random and asked their heights. The heights (in inches) are as follows: 67, 59, 64, 69, 65, 65, 66, 64, 62, 64, 62

Estimate the mean height of all female students at this college. Round your answer to the nearest tenth of an inch if necessary. A. It is not possible to estimate the population mean from this sample data

B. 64.3 inches C. 64.9 inches D. 63.7 inches

Question 33 of 40 A sample of 64 statistics students at a small college had a mean mathematics ACT score of 28 with a standard deviation of 4. Estimate the mean mathematics ACT score for all statistics students at this college. Give the 95% confidence interval.

A. 28.0 to 30.0 B. 25.0 to 27.0 C. 29.0 to 31.0 D. 27.0 to 29.0

Question 35 of 40 A researcher wishes to estimate the mean amount of money spent per month on food by households in a certain neighborhood. She desires a margin of error of $30. Past studies suggest that a population standard deviation of $248 is reasonable. Estimate the minimum sample size needed to estimate the population mean with the stated accuracy. A. 274 B. 284 C. 264 D. 272

Question 36 of 40 Monthly incomes of employees at a particular company have a mean of $5954. The distribution of sample means for samples of size 70 is normal with a mean of $5954 and a standard deviation of $259. Suppose you take a sample of size 70 employees from the company and find that their mean monthly income is $5747. How many standard deviations is the sample mean from the mean of the sampling distribution?

A. 0.8 standard deviations above the mean B. 0.8 standard deviations below the mean

C. 7.3 standard deviations below the mean C. 207 standard deviations below the mean

Question 37 of 40 A sample of nine students is selected from among the students taking a particular exam. The nine students were asked how much time they had spent studying for the exam and the responses (in hours) were as follows: 18, 7, 10, 13, 12, 16, 5, 20, 21

Estimate the mean study time of all students taking the exam. Round your answer to the nearest tenth of an hour if necessary. A. 13 hours B. 12.2 hours C. 13.6 hours

D. It is not possible to estimate the population mean from this sample data

Question 38 of 40 Among a random sample of 150 employees of a particular company, the mean commute distance is 29.6 miles. This mean lies 1.2 standard deviations above the mean of the sampling distribution. If a second sample of 150 employees is selected, what is the probability that for the second sample, the mean commute distance will be less than 29.6 miles? A. 0.8849 B. 0.5 C. 0.1131

D. 0.1151

Question 39 of 40 Sample size = 400, sample mean = 44, sample standard deviation = 16. What is the margin of error? A. 1.4 B. 1.6 C. 2.2 D. 2.6

In the first series of rolls of a die, the number of odd numbers exceeded the number of even numbers by 5. In the second series of rolls of the same die, the number of odd numbers exceeded the number of even numbers by 11. Determine which series is closer to the 50/50 ratio of odd/even expected of a fairly rolled die.

A. The second series is closer because the difference between odd and even numbers is greater than the difference for the first series.

B. The first series is closer because the difference between odd and even numbers is less than the difference for the second series.

C. Since 1/2 1/5 1/11, the first series is closer.

D. The series closer to the theoretical 50/50 cannot be determined unless the total number of rolls for both series is given

Question 2 of 40

A class consists of 50 women and 82 men. If a student is randomly

selected, what is the probability that the student is a woman?

A. 32/132

B. 27/66

C. 50/132

D. 82/132

Question 3 of 40

Suppose you have an extremely unfair die: The probability of a 6 is 3/8, and the probability of each other number is 1/8. If you toss the die 32 times, how many twos do you expect to see?

A. 2 B. 4 C. 3 D. 5

Question 4 of 40 If a person is randomly selected, find the probability that his or her birthday is not in May. Ignore leap years. There are 365 days in a year. Express your answer as a fraction.

A. 335/365 B. 334/365 C. 336/365 D. 30/365

Question 5 of 40

The data set represents the income levels of the members of a country club. Estimate the probability that a randomly selected member earns at least $98,000. 112,000 126,000 90,000 133,000 94,000 112,000 98,000 82,000 147,000 182,000 86,000 105,000 140,000 94,000 126,000 119,000 98,000 154,000 78,000 119,000

A. 0.4 B. 0.6 C. 0.66 D. 0.7

Question 6 of 40

If you flip a coin three times, the possible outcomes are HHH, HHT, HTH, HTT, THH, THT, TTH, TTT. What is the probability of getting at least one head?

A. 4/9 B. 5/6 C. 7/8 D. 5/8

Question 7 of 40

A study of 600 college students taking Statistics 101 revealed that 54 students received the grade of A. Typically 10% of the class gets an A. The difference between this group of students and the expected value is not significant at the 0.05 level. What does this mean in this case?

A. The probability that the difference occurred due to chance is less than 0.05.

B. The probability of getting an A is 10% and only 9% got an A in this study. The difference is less than 5% so it is not significant.

C. There is not enough information to make any conclusion.

D. The probability that the difference occurred due to chance is more than 0.05.

Question 8 of 40 On a multiple choice test, each question has 6 possible answers. If you make a random guess on the first question, what is the probability that you are correct?

A. 1/5 B. 1/6 C. 1/4 D. 2/5

Question 9 of 40

Suppose you buy 1 ticket for $1 out of a lottery of 1000 tickets where the prize for the one winning ticket is to be $500. What is your expected value? A. $0.00 B. −$0.40 C. −$1.00 D. −$0.50

Question 10 of 40

If you flip a coin three times, the possible outcomes are HHH, HHT, HTH, HTT, THH, THT, TTH, TTT. What is the probability of getting at least two tails?

A. 1/2 B. 2/3 C. 3/4 D. 4/9

Question 11 of 40 A study of students taking Statistics 101 was done. Four hundred students who studied for more than 10 hours averaged a B. Two hundred students who studied for less than 10 hours averaged a C. This difference was significant at the 0.01 level. What does this mean?

A. The probability that the difference was due to chance alone is greater than 0.01.

B. There is less than a 0.01 chance that the first group’s grades were better by chance alone.

C. The improvement was due to the fact that more people studied.

D. There is not enough information to make any conclusion.

Question 12 of 40 Of 1308 people who came into a blood bank to give blood, 314 people had high blood pressure. Estimate the probability that the next person who comes in to give blood will have high blood pressure (to 3 decimal places). A. 0.250 B. 0.490 C. 0.240 D. 0.160

Question 13 of 40 Suppose you pay $1.00 to roll a fair die with the understanding that you will get back $3.00 for rolling a 5 or a 2, nothing otherwise. What is your expected value?

A. $1.00 B. $0.00 C. $3.00 D. −$1.00

Question 14 of 40 A 28-year-old man pays $125 for a one-year life insurance policy with coverage of $140,000. If the probability that he will live through the year is 0.9994, to the nearest dollar, what is the man’s expected value for the insurance policy?

A. $139,916 B. −$41 C. $84 D. −$124

Question 15 of 40 Based on meteorological records, the probability that it will snow in a certain town on January 1st is 0.413. Find the probability that in a given year it will not snow on January 1st in that town. A. 0.345 B. 0.425 C. 0.587 D. 0.592

Question 16 of 40 Suppose you have an extremely unfair coin: the probability of a head is 1/5, and the probability of a tail is 4/5. If you toss the coin 40 times, how many heads do you expect to see?

A. 8 B. 6 C. 5 D. 4

Question 17 of 40 The probability that Luis will pass his statistics test is 0.94. Find the probability that he will fail his statistics test. A. 0.02 B. 0.05 C. 0.94 D. 0.06

Question 18 of 40 Suppose you have an extremely unfair coin: the probability of a head is 1/3 and the probability of a tail is 2/3. If you toss the coin 72 times, how many heads do you expect to see?

A. 12 B. 22 C. 24 D. 26

Question 19 of 40

A committee of three people is to be formed. The three people will be selected from a list of five possible committee members. A simple random sample of three people is taken, without replacement, from the group of five people. Using the letters A, B, C, D, E to represent the five people, list the possible samples of size three and use your list to determine the probability that B is included in the sample. (Hint: There are 10 possible samples.) A. 0.6 B. 0.4 C. 0.7 D. 0.8

Question 20 of 40 A die with 12 sides is rolled. What is the probability of rolling a number less than 11? Is this the same as rolling a total less than 11 with two six-sided dice? Explain. A. 2/6 B. 3/6

C. 4/6 D. 5/6

Question 21 of 40 A researcher wishes to estimate the proportion of college students who cheat on exams. A poll of 490 college students showed that 33% of them had, or intended to, cheat on examinations. Find the margin of error for the 95% confidence interval.

A. 0.0432 B. 0.0434 C. 0.0425 D. 0.0427

Question 23 of 40 A random sample of 30 households was selected from a particular neighborhood. The number of cars for each household is shown below. Estimate the mean number of cars per household for the population of households in this neighborhood. Give the 95% confidence interval.

2 0 1 2 3 2 1 0 1 4

1 3 2 0 1 1 2 3 1 2

1 0 2 3 0 2 2 1 0 2

A. 1.14 to 1.88 B. 1.12 to 1.88 C. 1.12 to 1.98 D. 1.14 to 1.98

Question 24 of 40 In a poll of 400 voters in a certain state, 61% said that they opposed a voter ID bill that might hinder some legitimate voters from voting. The margin of error in the poll was reported as 4 percentage points (with a 95% degree of confidence). Which statement is correct?

A. The reported margin of error is consistent with the sample size. B. There is not enough information to determine whether the margin of error is consistent with the sample size. C. The sample size is too small to achieve the stated margin of error. D. For the given sample size, the margin of error should be smaller than stated.

Question 27 of 40 30% of the fifth grade students in a large school district read below grade level. The distribution of sample proportions of samples of 100 students from this population is normal with a mean of 0.30 and a standard deviation of 0.045. Suppose that you select a sample of 100 fifth grade students from this district and find that the proportion that reads below grade level in the sample is 0.36. What is the probability that a second sample would be selected with a proportion less than 0.36?

A. 0.8932 B. 0.8920 C. 0.9032 D. 0.9048

Question 31 of 40 A population proportion is to be estimated. Estimate the minimum sample size needed to achieve a margin of error E = 0.01with a 95% degree of confidence.

A. 7,000 B. 8,000 C. 9,000 D. 10,000

Question 32 of 40 Eleven female college students are selected at random and asked their heights. The heights (in inches) are as follows: 67, 59, 64, 69, 65, 65, 66, 64, 62, 64, 62

Estimate the mean height of all female students at this college. Round your answer to the nearest tenth of an inch if necessary. A. It is not possible to estimate the population mean from this sample data

B. 64.3 inches C. 64.9 inches D. 63.7 inches

Question 33 of 40 A sample of 64 statistics students at a small college had a mean mathematics ACT score of 28 with a standard deviation of 4. Estimate the mean mathematics ACT score for all statistics students at this college. Give the 95% confidence interval.

A. 28.0 to 30.0 B. 25.0 to 27.0 C. 29.0 to 31.0 D. 27.0 to 29.0

Question 35 of 40 A researcher wishes to estimate the mean amount of money spent per month on food by households in a certain neighborhood. She desires a margin of error of $30. Past studies suggest that a population standard deviation of $248 is reasonable. Estimate the minimum sample size needed to estimate the population mean with the stated accuracy. A. 274 B. 284 C. 264 D. 272

Question 36 of 40 Monthly incomes of employees at a particular company have a mean of $5954. The distribution of sample means for samples of size 70 is normal with a mean of $5954 and a standard deviation of $259. Suppose you take a sample of size 70 employees from the company and find that their mean monthly income is $5747. How many standard deviations is the sample mean from the mean of the sampling distribution?

A. 0.8 standard deviations above the mean B. 0.8 standard deviations below the mean

C. 7.3 standard deviations below the mean C. 207 standard deviations below the mean

Question 37 of 40 A sample of nine students is selected from among the students taking a particular exam. The nine students were asked how much time they had spent studying for the exam and the responses (in hours) were as follows: 18, 7, 10, 13, 12, 16, 5, 20, 21

Estimate the mean study time of all students taking the exam. Round your answer to the nearest tenth of an hour if necessary. A. 13 hours B. 12.2 hours C. 13.6 hours

D. It is not possible to estimate the population mean from this sample data

Question 38 of 40 Among a random sample of 150 employees of a particular company, the mean commute distance is 29.6 miles. This mean lies 1.2 standard deviations above the mean of the sampling distribution. If a second sample of 150 employees is selected, what is the probability that for the second sample, the mean commute distance will be less than 29.6 miles? A. 0.8849 B. 0.5 C. 0.1131

D. 0.1151

Question 39 of 40 Sample size = 400, sample mean = 44, sample standard deviation = 16. What is the margin of error? A. 1.4 B. 1.6 C. 2.2 D. 2.6

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