# A sample space consists of 46 separate events that are - Expert Work

A sample space consists of 46 separate events that are equally likely. What is the probability of each?

A. 1/24

B. 1/46

C. 1/32

D. 1/18

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

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

In a poll, respondents were asked whether they had ever been in a car accident. 220 respondents indicated that they had been in a car accident and 370 respondents said that they had not been in a car accident. If one of these respondents is randomly selected, what is the probability of getting someone who has been in a car accident? Round to the nearest thousandth.

A. 0.384

B. 0.380

C. 0.373

D. 0.370

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

The distribution of B.A. degrees conferred by a local college is listed below, by major.

Major Frequency

English 2073

Mathematics 2164

Chemistry 318

Physics 856

Liberal Arts 1358

Business 1676

Engineering 868

9313

What is the probability that a randomly selected degree is not in Business?

A. 0.7800

B. 0.8200

C. 0.8300

D. 0.9200

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.

Jody checked the temperature 12 times on Monday, and the last digit of the temperature was odd six times more than it was even. On Tuesday, she checked it 18 times and the last digit was odd eight times more than it was even. Determine which series is closer to the 50/50 ratio of odd/even expected of such a series of temperature checks.

A. The Monday series is closer because 1/6 is closer to 1/2 than is 1/8.

B. The Monday series is closer because 6/12 is closer to 0.5 than is 8/18.

C. The Tuesday series is closer because the 13/18 is closer to 0.5 than is 9/12.

D. The series closest to the theoretical 50/50 cannot be determined without knowing the number of odds and evens in each series.

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

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

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

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

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

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

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

Joe dealt 20 cards from a standard 52-card deck, and the number of red cards exceeded the number of black cards by 8. He reshuffled the cards and dealt 30 cards. This time, the number of red cards exceeded the number of black cards by 10. Determine which deal is closer to the 50/50 ratio of red/black expected of fairly dealt hands from a fair deck and why.

A. The first series is closer because 1/10 is farther from 1/2 than is 1/8.

B. The series closer to the theoretical 50/50 cannot be determined unless the number of red and black cards for each deal is given.

C. The second series is closer because 20/30 is closer to 1/2 than is 14/20.

D. The first series is closer because the difference between red and black is smaller than the difference in the second series.

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

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

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

A. 1/8

B. 3/8

C. 5/8

D. 6/8

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

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

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

Suggest the cause of the correlation among the data.

The graph shows strength of coffee (y) and number of scoops used to make 10 cups of coffee (x). Identify the probable cause of the correlation.

A.

The variation in the x variable is a direct cause of the variation in

the y variable.

B. There is no correlation between the variables.

C. The correlation is due to a common underlying cause.

D. The correlation between the variables is coincidental.

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

D. 207 standard deviations below the mean

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

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

Select the best fit line on the scatter diagram below.

A. A

B. B

C. C

D. All of the lines are equally good

Select the best estimate of the correlation coefficient for the data depicted in the scatter diagram.

A. 0.60

B. -0.97

C. 0.10

D. -0.60

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

Of the 6796 students in one school district, 1537 cannot read up to grade level. Among a sample of 812 of the students from this school district, 211 cannot read up to grade level. Find the sample proportion of students who cannot read up to grade level.

A. 0.14

B. 0.26

C. 211

D. 0.23

The scatter plot and best-fit line show the relation among the number of cars waiting by a school (y) and the amount of time after the end of classes (x) in arbitrary units. The correlation coefficient is -0.55. Determine the amount of variation in the number of cars not explained by the variation time after school.

A. 55%

B. 70%

C. 30%

D. 45%

The scatter plot and best-fit line show the relation between the price per item (y) and the availability of that item (x) in arbitrary units. The correlation coefficient is -0.95. Determine the amount of variation in pricing explained by the variation in availability.

A. 5%

B. 10%

C. 95%

D. 90%

A researcher wishes to estimate the proportion of college students who cheat on exams. A poll of 560 college students showed that 27% of them had, or intended to, cheat on examinations. Find the 95% confidence interval.

A. 0.2323 to 0.3075

B. 0.2325 to 0.3075

C. 0.2325 to 0.3185

D. 0.2323 to 0.3185

The scatter plot and best-fit line show the relation among the data for the price of a stock (y) and employment (x) in arbitrary units. The correlation coefficient is 0.8. Predict the stock price for an employment value of 6.

A. 8.8

B. 6.2

C. 8.2

D. None of the values are correct

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

Write possible coordinates for the single outlier such that it would no longer be an outlier.

A. (23, 18)

B. (20, 5)

C. (15, 15)

D. (12, 15)

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.

A. 1.14 to 1.88

B. 1.12 to 1.88

C. 1.12 to 1.98

D. 1.14 to 1.98

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

The scatter plot and best-fit line show the relation among the number of cars waiting by a school (y) and the amount of time after the end of classes (x) in arbitrary units. The correlation coefficient is -0.55. Use the line of best fit to predict the number of cars at time 4 after the end of classes.

A. 7.0

B. 6.0

C. 8.0

D. 3.5

Select the best fit line on the scatter diagram below.

A. A

B. B

C. C

D. None of the lines is the line of best fit

A. 1/24

B. 1/46

C. 1/32

D. 1/18

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

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

In a poll, respondents were asked whether they had ever been in a car accident. 220 respondents indicated that they had been in a car accident and 370 respondents said that they had not been in a car accident. If one of these respondents is randomly selected, what is the probability of getting someone who has been in a car accident? Round to the nearest thousandth.

A. 0.384

B. 0.380

C. 0.373

D. 0.370

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

The distribution of B.A. degrees conferred by a local college is listed below, by major.

Major Frequency

English 2073

Mathematics 2164

Chemistry 318

Physics 856

Liberal Arts 1358

Business 1676

Engineering 868

9313

What is the probability that a randomly selected degree is not in Business?

A. 0.7800

B. 0.8200

C. 0.8300

D. 0.9200

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.

Jody checked the temperature 12 times on Monday, and the last digit of the temperature was odd six times more than it was even. On Tuesday, she checked it 18 times and the last digit was odd eight times more than it was even. Determine which series is closer to the 50/50 ratio of odd/even expected of such a series of temperature checks.

A. The Monday series is closer because 1/6 is closer to 1/2 than is 1/8.

B. The Monday series is closer because 6/12 is closer to 0.5 than is 8/18.

C. The Tuesday series is closer because the 13/18 is closer to 0.5 than is 9/12.

D. The series closest to the theoretical 50/50 cannot be determined without knowing the number of odds and evens in each series.

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

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

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

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

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

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

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

Joe dealt 20 cards from a standard 52-card deck, and the number of red cards exceeded the number of black cards by 8. He reshuffled the cards and dealt 30 cards. This time, the number of red cards exceeded the number of black cards by 10. Determine which deal is closer to the 50/50 ratio of red/black expected of fairly dealt hands from a fair deck and why.

A. The first series is closer because 1/10 is farther from 1/2 than is 1/8.

B. The series closer to the theoretical 50/50 cannot be determined unless the number of red and black cards for each deal is given.

C. The second series is closer because 20/30 is closer to 1/2 than is 14/20.

D. The first series is closer because the difference between red and black is smaller than the difference in the second series.

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

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

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

A. 1/8

B. 3/8

C. 5/8

D. 6/8

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

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

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

Suggest the cause of the correlation among the data.

The graph shows strength of coffee (y) and number of scoops used to make 10 cups of coffee (x). Identify the probable cause of the correlation.

A.

The variation in the x variable is a direct cause of the variation in

the y variable.

B. There is no correlation between the variables.

C. The correlation is due to a common underlying cause.

D. The correlation between the variables is coincidental.

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

D. 207 standard deviations below the mean

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

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

Select the best fit line on the scatter diagram below.

A. A

B. B

C. C

D. All of the lines are equally good

Select the best estimate of the correlation coefficient for the data depicted in the scatter diagram.

A. 0.60

B. -0.97

C. 0.10

D. -0.60

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

Of the 6796 students in one school district, 1537 cannot read up to grade level. Among a sample of 812 of the students from this school district, 211 cannot read up to grade level. Find the sample proportion of students who cannot read up to grade level.

A. 0.14

B. 0.26

C. 211

D. 0.23

The scatter plot and best-fit line show the relation among the number of cars waiting by a school (y) and the amount of time after the end of classes (x) in arbitrary units. The correlation coefficient is -0.55. Determine the amount of variation in the number of cars not explained by the variation time after school.

A. 55%

B. 70%

C. 30%

D. 45%

The scatter plot and best-fit line show the relation between the price per item (y) and the availability of that item (x) in arbitrary units. The correlation coefficient is -0.95. Determine the amount of variation in pricing explained by the variation in availability.

A. 5%

B. 10%

C. 95%

D. 90%

A researcher wishes to estimate the proportion of college students who cheat on exams. A poll of 560 college students showed that 27% of them had, or intended to, cheat on examinations. Find the 95% confidence interval.

A. 0.2323 to 0.3075

B. 0.2325 to 0.3075

C. 0.2325 to 0.3185

D. 0.2323 to 0.3185

The scatter plot and best-fit line show the relation among the data for the price of a stock (y) and employment (x) in arbitrary units. The correlation coefficient is 0.8. Predict the stock price for an employment value of 6.

A. 8.8

B. 6.2

C. 8.2

D. None of the values are correct

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

Write possible coordinates for the single outlier such that it would no longer be an outlier.

A. (23, 18)

B. (20, 5)

C. (15, 15)

D. (12, 15)

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.

A. 1.14 to 1.88

B. 1.12 to 1.88

C. 1.12 to 1.98

D. 1.14 to 1.98

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

The scatter plot and best-fit line show the relation among the number of cars waiting by a school (y) and the amount of time after the end of classes (x) in arbitrary units. The correlation coefficient is -0.55. Use the line of best fit to predict the number of cars at time 4 after the end of classes.

A. 7.0

B. 6.0

C. 8.0

D. 3.5

Select the best fit line on the scatter diagram below.

A. A

B. B

C. C

D. None of the lines is the line of best fit

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