Deck 22: Binomial Distribution and Normal Approximation

Question 1

You can use the Poisson distribution to approximate the binomial distribution when the sample size is large and the probability of an event of interest is very small.

Answer 1

True

Question 2

When you use the Poisson distribution to approximate the binomial distribution,the number of events of interest can be larger than the sample size.

Answer 2

False

Question 3

When you use the Poisson distribution to approximate the binomial distribution,the mean is n $\pi$ where n is the sample size and $\pi$ is the probability of an event of interest.

Answer 3

True

Question 4

When you use the Poisson distribution to approximate the binomial distribution,the standard deviation is n $\pi$ where n is the sample size and $\pi$ is the probability of an event of interest.

Question 5

Based on past experience,only 0.5% of the invoices of a company contain an error.Out of the 1,500 invoices that the company will issue,what is the approximate probability that zero invoices will contain an error?

Question 6

Based on past experience,only 0.5% of the invoices of a company contain an error.Out of the 1,500 invoices that the company will issue,what is the approximate probability that exactly 2 invoices will contain an error?

Question 7

Based on past experience,only 0.5% of the invoices of a company contain an error.Out of the 1,500 invoices that the company will issue,what is the approximate probability that less than 4 invoices will contain an error?

Question 8

Based on past experience,only 0.5% of the invoices of a company contain an error.Out of the 1,500 invoices that the company will issue,what is the approximate probability that no more than 4 invoices will contain an error?

Question 9

Based on past experience,only 0.5% of the invoices of a company contain an error.Out of the 1,500 invoices that the company will issue,what is the approximate probability that at least 4 invoices will contain an error?

Question 10

Based on past experience,only 0.5% of the invoices of a company contain an error.Out of the 1,500 invoices that the company will issue,what is the approximate probability that more than 4 invoices will contain an error?

Question 11

If a new machine of a production plant is functioning properly,only 1% of the items produced will be defective.Out of the 1,000 items the plant produces on a single day,the approximate probability that none of the items will be defective if the new machine is indeed functioning properly is .

Question 12

If a new machine of a production plant is functioning properly,only 1% of the items produced will be defective.Out of the 1,000 items the plant produces on a single day,the approximate probability that exactly 0.2% of the items will be defective if the new machine is indeed functioning properly is .

Question 13

If a new machine of a production plant is functioning properly,only 1% of the items produced will be defective.Out of the 1,000 items the plant produces on a single day,the approximate probability that no more than 0.2% of the items will be defective if the new machine is indeed functioning properly is .

Question 14

If a new machine of a production plant is functioning properly,only 1% of the items produced will be defective.Out of the 1,000 items the plant produces on a single day,the approximate probability that less than 0.2% of the items will be defective if the new machine is indeed functioning properly is .

Question 15

If a new machine of a production plant is functioning properly,only 1% of the items produced will be defective.Out of the 1,000 items the plant produces on a single day,the approximate probability that at least 0.2% of the items will be defective if the new machine is indeed functioning properly is .

Question 16

If a new machine of a production plant is functioning properly,only 1% of the items produced will be defective.Out of the 1,000 items the plant produces on a single day,the approximate probability that more than 0.2% of the items will be defective if the new machine is indeed functioning properly is .

Question 17

One of the reasons that a correction for continuity adjustment is needed when approximating the binomial distribution with a normal distribution is because the normal distribution is used for a discrete random variable while the binomial distribution is used for a continuous random variable.

Question 18

One of the reasons that a correction for continuity adjustment is needed when approximating the binomial distribution with a normal distribution is because the probability of getting a specific value of a random variable is zero with the normal distribution.

Question 19

One of the reasons that a correction for continuity adjustment is needed when approximating the binomial distribution with a normal distribution is because a random variable having a binomial distribution can have only a specified value while a random variable having a normal distribution can take on any values within an interval around that specified value.

Question 20

To determine the probability of getting fewer than 3 events of interest in a binomial distribution,you will find the area under the normal curve for X = 3.5 and below.

Question 21

To determine the probability of getting more than 3 events of interest in a binomial distribution,you will find the area under the normal curve for X = 3.5 and above.

Question 22

To determine the probability of getting at least 3 events of interest in a binomial distribution,you will find the area under the normal curve for X = 2.5 and above.

Question 23

To determine the probability of getting no more than 3 events of interest in a binomial distribution,you will find the area under the normal curve for X = 2.5 and below.

Question 24

To determine the probability of getting between 3 and 4 events of interest in a binomial distribution,you will find the area under the normal curve between X = 3.5 and 4.5.

Question 25

To determine the probability of getting between 2 and 4 events of interest in a binomial distribution,you will find the area under the normal curve between X = 1.5 and 4.5.

Question 26

As a general rule,one can use the normal distribution to approximate a binomial distribution whenever the sample size is at least 30.

Question 27

As a general rule,one can use the normal distribution to approximate a binomial distribution whenever the sample size is at least 15.

Question 28

As a general rule,one can use the normal distribution to approximate a binomial distribution whenever n $\pi$ is at least 5.

Question 29

As a general rule,one can use the normal distribution to approximate a binomial distribution whenever n( $\pi$ -1) is at least 5.

Question 30

As a general rule,one can use the normal distribution to approximate a binomial distribution whenever n $\pi$ and n( $\pi$ -1) are at least 5.

Question 31

SCENARIO 6-7
A company has 125 personal computers.The probability that any one of them will require repair on a given day is 0.15.
Referring to Scenario 6-7,which of the following is one of the properties required so that the binomial distribution can be used to compute the probability that no more than 2 computers will require repair on a given day?

A)The number of personal computers the company owns on a given day is fixed.
B)The probability that a computer that will require repair in the morning is the same as that in the afternoon.
C)The number of computers that will require repair in the morning is independent of the number of computers that will require repair in the afternoon.
D)The probability that two or more computers that will require repair in a given day approaches zero.

Question 32

SCENARIO 6-7
A company has 125 personal computers.The probability that any one of them will require repair on a given day is 0.15.
Referring to Scenario 6-7,which of the following is one of the properties required so that the binomial distribution can be used to compute the probability that no more than 2 computers will require repair on a given day?

A)The probability that a computer that will require repair in the morning is the same as that in the afternoon.
B)A randomly selected computer on a given day will either require a repair or will not.
C)The number of computers that will require repair in the morning is independent of the number of computers that will require repair in the afternoon.
D)The probability that two or more computers that will require repair in a given day approaches zero.

Question 33

SCENARIO 6-7
A company has 125 personal computers.The probability that any one of them will require repair on a given day is 0.15.
Referring to Scenario 6-7,which of the following is one of the properties required so that the binomial distribution can be used to compute the probability that no more than 2 computers will require repair on a given day?

A)The probability that a computer that will require repair in the morning is the same as that in the afternoon.
B)The number of computers that will require repair in the morning is independent of the number of computers that will require repair in the afternoon.
C)The probability that any one of the computers that will require repair on a given day will not affect or change the probability that any other computers that will require repair on the same day.
D)The probability that two or more computers that will require repair in a given day approaches zero.

Question 34

SCENARIO 6-7
A company has 125 personal computers.The probability that any one of them will require repair on a given day is 0.15.
Referring to Scenario 6-7 and assuming that the number of computers that requires repair on a given day follows a binomial distribution,compute the probability that there will be no more than 8 computers that require repair on a given day using a normal approximation.

Question 35

SCENARIO 6-7
A company has 125 personal computers.The probability that any one of them will require repair on a given day is 0.15.
Referring to Scenario 6-7 and assuming that the number of computers that requires repair on a given day follows a binomial distribution,compute the probability that there will be less than 8 computers that require repair on a given day using a normal approximation.

Question 36

SCENARIO 6-7
A company has 125 personal computers.The probability that any one of them will require repair on a given day is 0.15.
Referring to Scenario 6-7 and assuming that the number of computers that requires repair on a given day follows a binomial distribution,compute the probability that there will be exactly 10 computers that require repair on a given day using a normal approximation.

Question 37

SCENARIO 6-7
A company has 125 personal computers.The probability that any one of them will require repair on a given day is 0.15.
Referring to Scenario 6-7 and assuming that the number of computers that requires repair on a given day follows a binomial distribution,compute the probability that there will be at least 25 computers that require repair on a given day using a normal approximation.

Question 38

SCENARIO 6-7
A company has 125 personal computers.The probability that any one of them will require repair on a given day is 0.15.
Referring to Scenario 6-7 and assuming that the number of computers that requires repair on a given day follows a binomial distribution,compute the probability that there will be more than 25 computers that require repair on a given day using a normal approximation.

Question 39

SCENARIO 6-7
A company has 125 personal computers.The probability that any one of them will require repair on a given day is 0.15.
Referring to Scenario 6-7 and assuming that the number of computers that requires repair on a given day follows a binomial distribution,compute the probability that there will be between 25 and 30 computers that require repair on a given day using a normal approximation.

Question 40

SCENARIO 6-7
A company has 125 personal computers.The probability that any one of them will require repair on a given day is 0.15.
Referring to Scenario 6-7 and assuming that the number of computers that requires repair on a given day follows a binomial distribution,compute the probability that there will be more than 25 but less than 30 computers that require repair on a given day using a normal approximation.

Question 41

SCENARIO 6-7
A company has 125 personal computers.The probability that any one of them will require repair on a given day is 0.15.
Referring to Scenario 6-7 and assuming that the number of computers that requires repair on a given day follows a binomial distribution,compute the probability that there will be less than 25 or more than 30 computers that require repair on a given day using a normal approximation.

Question 42

The use of the finite population correction factor when sampling without replacement from finite populations will

A)increase the standard error of the mean.
B)not affect the standard error of the mean.
C)reduce the standard error of the mean.
D)only affect the proportion,not the mean.

Question 43

You use the finite population correction factor when

A)you sample without replacement and the sample size is larger than 5% of the population size.
B)you sample without replacement and the sample size is smaller than 5% of the population size.
C)you sample with replacement and the sample size is larger than 5% of the population size.
D)you sample with replacement and the sample size is smaller than 5% of the population size.

Question 44

The finite population correction factor is

A)
B)
C)
D)

Question 45

SCENARIO 7-7
Times spent studying by students in the week before final exams follow a normal distribution with standard deviation 8 hours.A random sample of 4 students was taken from a population of 50 in order to estimate the mean study time for the population of all students.Use the finite population correction.
Referring to Scenario 7-7,what is the standard error of all the sample means?

Question 46

SCENARIO 7-7
Times spent studying by students in the week before final exams follow a normal distribution with standard deviation 8 hours.A random sample of 4 students was taken from a population of 50 in order to estimate the mean study time for the population of all students.Use the finite population correction.
Referring to Scenario 7-7,what is the probability that the sample mean exceeds the population mean by more than 2 hours?

Question 47

SCENARIO 7-7
Times spent studying by students in the week before final exams follow a normal distribution with standard deviation 8 hours.A random sample of 4 students was taken from a population of 50 in order to estimate the mean study time for the population of all students.Use the finite population correction.
Referring to Scenario 7-7,what is the probability that the sample mean is more than 3 hours below the population mean?

Question 48

SCENARIO 7-7
Times spent studying by students in the week before final exams follow a normal distribution with standard deviation 8 hours.A random sample of 4 students was taken from a population of 50 in order to estimate the mean study time for the population of all students.Use the finite population correction.
Referring to Scenario 7-7,what is the probability that the sample mean differs from the population mean by less than 2 hours?

Question 49

SCENARIO 7-7
Times spent studying by students in the week before final exams follow a normal distribution with standard deviation 8 hours.A random sample of 4 students was taken from a population of 50 in order to estimate the mean study time for the population of all students.Use the finite population correction.
Referring to Scenario 7-7,what is the probability that the sample mean differs from the population mean by more than 3 hours?

Question 50

SCENARIO 7-7
Times spent studying by students in the week before final exams follow a normal distribution with standard deviation 8 hours.A random sample of 4 students was taken from a population of 50 in order to estimate the mean study time for the population of all students.Use the finite population correction.
Referring to Scenario 7-7,5% of all the samples of 4 will have a sample mean of at least how many hours above the population mean?

Question 51

SCENARIO 7-7
Times spent studying by students in the week before final exams follow a normal distribution with standard deviation 8 hours.A random sample of 4 students was taken from a population of 50 in order to estimate the mean study time for the population of all students.Use the finite population correction.
Referring to Scenario 7-7,10% of all the samples of size 4 will have a sample mean of at least how many hours below the population mean?

Question 52

SCENARIO 7-7
Times spent studying by students in the week before final exams follow a normal distribution with standard deviation 8 hours.A random sample of 4 students was taken from a population of 50 in order to estimate the mean study time for the population of all students.Use the finite population correction.
Referring to Scenario 7-7,90% of all the samples of size 4 will have a sample mean of no more than how many hours from the population mean?

Question 53

SCENARIO 7-7
Times spent studying by students in the week before final exams follow a normal distribution with standard deviation 8 hours.A random sample of 4 students was taken from a population of 50 in order to estimate the mean study time for the population of all students.Use the finite population correction.
Referring to Scenario 7-7,80% of all the samples of 4 will have a sample mean of no more than how many hours from the population mean?

Question 54

SCENARIO 7-8
According to a survey,only 15% of customers who visited the web site of a major retail store made a purchase.Random samples of size 50 are selected from a population of 900.Use the finite population correction factor.
Referring to Scenario 7-8,the mean of all the sample proportions of 50 customers who will make a purchase after visiting the web site is .

Question 55

SCENARIO 7-8
According to a survey,only 15% of customers who visited the web site of a major retail store made a purchase.Random samples of size 50 are selected from a population of 900.Use the finite population correction factor.
Referring to Scenario 7-8,the standard error of all the sample proportions of customers who will make a purchase after visiting the web site is .

Question 56

SCENARIO 7-8
According to a survey,only 15% of customers who visited the web site of a major retail store made a purchase.Random samples of size 50 are selected from a population of 900.Use the finite population correction factor.
Referring to Scenario 7-8,the requirements for using a normal distribution to approximate a binomial distribution is fulfilled.

Question 57

SCENARIO 7-8
According to a survey,only 15% of customers who visited the web site of a major retail store made a purchase.Random samples of size 50 are selected from a population of 900.Use the finite population correction factor.
Referring to Scenario 7-8,what proportion of the samples will have between 20% and 30% of customers who will make a purchase after visiting the web site?

Question 58

SCENARIO 7-8
According to a survey,only 15% of customers who visited the web site of a major retail store made a purchase.Random samples of size 50 are selected from a population of 900.Use the finite population correction factor.
Referring to Scenario 7-8,what proportion of the samples will have less than 15% of customers who will make a purchase after visiting the web site?

Question 59

SCENARIO 7-8
According to a survey,only 15% of customers who visited the web site of a major retail store made a purchase.Random samples of size 50 are selected from a population of 900.Use the finite population correction factor.
Referring to Scenario 7-8,what is the probability that a random sample of 50 will have at least 30% of customers who will make a purchase after visiting the web site?

Question 60

SCENARIO 7-8
According to a survey,only 15% of customers who visited the web site of a major retail store made a purchase.Random samples of size 50 are selected from a population of 900.Use the finite population correction factor.
Referring to Scenario 7-8,90% of the samples will have less than what percentage of customers who will make a purchase after visiting the web site?

Question 61

SCENARIO 7-8
According to a survey,only 15% of customers who visited the web site of a major retail store made a purchase.Random samples of size 50 are selected from a population of 900.Use the finite population correction factor.
Referring to Scenario 7-8,90% of the samples will have more than what percentage of customers who will make a purchase after visiting the web site?

Question 62

SCENARIO 8-12
The superintendent of a unified school district of a small town wants to make sure that no more than 5% of the students skip more than 10 days of school in a year.A random sample of 145 students from a population of 800 showed that 12 students skipped more than 10 days of school last year.
Referring to Scenario 8-12,what is the critical value for the 95% one-sided confidence interval for the proportion of students who skipped more than 10 days of school last year?

Question 63

SCENARIO 8-12
The superintendent of a unified school district of a small town wants to make sure that no more than 5% of the students skip more than 10 days of school in a year.A random sample of 145 students from a population of 800 showed that 12 students skipped more than 10 days of school last year.
Referring to Scenario 8-12,what is the upper bound of the 95% one-sided confidence interval for the proportion of students who skipped more than 10 days of school last year?

Question 64

SCENARIO 8-12
The superintendent of a unified school district of a small town wants to make sure that no more than 5% of the students skip more than 10 days of school in a year.A random sample of 145 students from a population of 800 showed that 12 students skipped more than 10 days of school last year.
Referring to Scenario 8-12,the superintendent can conclude with 95% level of confidence that no more than 5% of the students in the unified school district skipped more than 10 days of school last year.

Question 65

SCENARIO 8-13
The president of a university is concerned that illicit drug use on campus is higher than the 5% targeted level.A random sample of 250 students from a population of 2,000 revealed that 7 of them had used illicit drugs during the last 12 months.
Referring to Scenario 8-13,what is the critical value for the 90% one-sided confidence interval for the proportion of students who had used illicit drugs during the last 12 months?

Question 66

SCENARIO 8-13
The president of a university is concerned that illicit drug use on campus is higher than the 5% targeted level.A random sample of 250 students from a population of 2,000 revealed that 7 of them had used illicit drugs during the last 12 months.
Referring to Scenario 8-13,what is the upper bound of the 90% one-sided confidence interval for the proportion of students who had used illicit drugs during the last 12 months?

Question 67

SCENARIO 8-13
The president of a university is concerned that illicit drug use on campus is higher than the 5% targeted level.A random sample of 250 students from a population of 2,000 revealed that 7 of them had used illicit drugs during the last 12 months.
Referring to Scenario 8-13,the president can be 90% confident that no more than 5% of the students at the university had used illicit drugs during the last 12 months.

Question 68

SCENARIO 8-13
The president of a university is concerned that illicit drug use on campus is higher than the 5% targeted level.A random sample of 250 students from a population of 2,000 revealed that 7 of them had used illicit drugs during the last 12 months.
Referring to Scenario 8-13,using the 90% one-sided confidence interval,the president can be 95% confident that no more than 5% of the students at the university had used illicit drugs during the last 12 months.

Question 69

SCENARIO 8-13
The president of a university is concerned that illicit drug use on campus is higher than the 5% targeted level.A random sample of 250 students from a population of 2,000 revealed that 7 of them had used illicit drugs during the last 12 months.
Referring to Scenario 8-13,using the 90% one-sided confidence interval,the president can be 85% confident that no more than 5% of the students at the university had used illicit drugs during the last 12 months.

Question 70

SCENARIO 8-14
The president of a university is concerned that the percentage of students who have cheated on an exam is higher than the 1% acceptable level.A confidential random sample of 1,000 students from a population of 7,000 revealed that 6 of them said that they had cheated on an exam during the last semester.
Referring to Scenario 8-14,what is the critical value for the 90% one-sided confidence interval for the proportion of students who had cheated on an exam during the last 12 months?

Question 71

SCENARIO 8-14
The president of a university is concerned that the percentage of students who have cheated on an exam is higher than the 1% acceptable level.A confidential random sample of 1,000 students from a population of 7,000 revealed that 6 of them said that they had cheated on an exam during the last semester.
Referring to Scenario 8-14,what is the upper bound of the 90% one-sided confidence interval for the proportion of students who had cheated on an exam during the last 12 months?

Question 72

SCENARIO 8-14
The president of a university is concerned that the percentage of students who have cheated on an exam is higher than the 1% acceptable level.A confidential random sample of 1,000 students from a population of 7,000 revealed that 6 of them said that they had cheated on an exam during the last semester.
Referring to Scenario 8-14,the president can be 90% confident that no more than 1% of the students at the university had cheated on an exam during the last semester.

Question 73

SCENARIO 8-14
The president of a university is concerned that the percentage of students who have cheated on an exam is higher than the 1% acceptable level.A confidential random sample of 1,000 students from a population of 7,000 revealed that 6 of them said that they had cheated on an exam during the last semester.
Referring to Scenario 8-14,using the 90% one-sided confidence interval,the president can be 95% confident that no more than 1% of the students at the university had cheated on an exam during the last semester.

Question 74

SCENARIO 8-14
The president of a university is concerned that the percentage of students who have cheated on an exam is higher than the 1% acceptable level.A confidential random sample of 1,000 students from a population of 7,000 revealed that 6 of them said that they had cheated on an exam during the last semester.
Referring to Scenario 8-14,using the 90% one-sided confidence interval,the superintendent can be 85% confident that no more than 1% of the students at the university had cheated on an exam during the last semester.

Question 75

SCENARIO 8-15
A wealthy real estate investor wants to decide whether it is a good investment to build a high-end shopping complex in a suburban county in Chicago.His main concern is the total market value of the 3,605 houses in the suburban county.He commissioned a statistical consulting group to take a sample of 200 houses and obtained a sample mean market price of $225,000 and a sample standard deviation of $38,700.The consulting group also found out that the mean differences between market prices and appraised prices was $125,000 with a standard deviation of $3,400.Also,the proportion of houses in the sample that are appraised for higher than the market prices is 0.24.
Referring to Scenario 8-15,what will be the 90% confidence interval for the total difference between the market prices and appraised prices of the houses in the suburban county constructed by the consulting group?

Question 76

SCENARIO 8-15
A wealthy real estate investor wants to decide whether it is a good investment to build a high-end shopping complex in a suburban county in Chicago.His main concern is the total market value of the 3,605 houses in the suburban county.He commissioned a statistical consulting group to take a sample of 200 houses and obtained a sample mean market price of $225,000 and a sample standard deviation of $38,700.The consulting group also found out that the mean differences between market prices and appraised prices was $125,000 with a standard deviation of $3,400.Also,the proportion of houses in the sample that are appraised for higher than the market prices is 0.24.
Referring to Scenario 8-15,what will be the 90% confidence interval for the total market price of the houses in the suburban county constructed by the consulting group?

Question 77

SCENARIO 8-16
A random sample of 100 stores from a large chain of 500 garden supply stores was selected to determine the mean number of lawnmowers sold at an end-of-season clearance sale.The sample results indicated a mean of 6 and a standard deviation of 2 lawnmowers sold.A 95% confidence interval (5.623 to 6.377)was established based on these results.
Referring to Scenario 8-16,if the population had consisted of 1,000 stores,the confidence interval estimate of the mean with finite population correction would have been wider in range.

Question 78

SCENARIO 8-16
A random sample of 100 stores from a large chain of 500 garden supply stores was selected to determine the mean number of lawnmowers sold at an end-of-season clearance sale.The sample results indicated a mean of 6 and a standard deviation of 2 lawnmowers sold.A 95% confidence interval (5.623 to 6.377)was established based on these results.
Referring to Scenario 8-16,if the population had consisted of 400 stores,the confidence interval estimate of the mean with finite population correction would have been wider in range.

Question 79

SCENARIO 8-16
A random sample of 100 stores from a large chain of 500 garden supply stores was selected to determine the mean number of lawnmowers sold at an end-of-season clearance sale.The sample results indicated a mean of 6 and a standard deviation of 2 lawnmowers sold.A 95% confidence interval (5.623 to 6.377)was established based on these results.
Referring to Scenario 8-16,the confidence interval estimate of the mean with finite population correction will be wider in range than confidence interval estimate without finite population correction.

Question 80

SCENARIO 8-16
A random sample of 100 stores from a large chain of 500 garden supply stores was selected to determine the mean number of lawnmowers sold at an end-of-season clearance sale.The sample results indicated a mean of 6 and a standard deviation of 2 lawnmowers sold.A 95% confidence interval (5.623 to 6.377)was established based on these results.
Referring to Scenario 8-16,of all possible samples of 100 stores drawn from the population of 1,000 stores,95% of the sample means will fall between 5.623 and 6.377 lawnmowers.