Deck 19: Questions that Involve Online Topics

Question 1

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.

Answer 1

True

Question 2

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 ________.

Answer 2

0.002769

Question 3

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 ________.

Answer 3

0.002270

Question 4

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 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 exactly 2 invoices will contain an error?

Question 6

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

Question 7

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.

Question 8

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

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 less than 4 invoices will contain an error?

Question 10

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

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 less than 0.2% 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 none of the items will be defective if the new machine is indeed functioning properly is ________.

Question 13

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 14

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 15

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 16

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 17

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 18

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 19

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 20

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 21

TABLE 6-1
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 Table 6-1 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 22

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 23

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

Question 24

TABLE 6-1
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 Table 6-1 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 25

TABLE 6-1
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 Table 6-1 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 26

TABLE 6-1
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 Table 6-1 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 27

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

Question 28

TABLE 6-1
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 Table 6-1 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 29

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 30

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

Question 31

TABLE 6-1
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 Table 6-1 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 32

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

Question 33

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 34

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 35

TABLE 6-1
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 Table 6-1, 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 36

TABLE 6-1
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 Table 6-1 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 37

TABLE 6-1
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 Table 6-1, 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 38

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

Question 39

TABLE 6-1
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 Table 6-1, 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 40

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 41

TABLE 7-2
According to a survey, only 15% of customers who visited the website 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.
True or False: Referring to Table 7-2, the requirements for using a normal distribution to approximate a binomial distribution is fulfilled.

Question 42

TABLE 7-2
According to a survey, only 15% of customers who visited the website 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 Table 7-2, what proportion of the samples will have between 20% and 30% of customers who will make a purchase after visiting the website?

Question 43

TABLE 7-1
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 Table 7-1, what is the probability that the sample mean is more than 3 hours below the population mean?

Question 44

TABLE 7-2
According to a survey, only 15% of customers who visited the website 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 Table 7-2, 90% of the samples will have less than what percentage of customers who will make a purchase after visiting the website?

Question 45

TABLE 7-1
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 Table 7-1, 80% of all the samples of 4 will have a sample mean of no more than how many hours from the population mean?

Question 46

TABLE 7-1
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 Table 7-1, 10% of all the samples of 4 will have a sample mean of at least how many hours below the population mean?

Question 47

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 48

TABLE 7-2
According to a survey, only 15% of customers who visited the website 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 Table 7-2, 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 website?

Question 49

TABLE 7-2
According to a survey, only 15% of customers who visited the website 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 Table 7-2, the mean of all the sample proportions of 50 customers who will make a purchase after visiting the website is ________.

Question 50

TABLE 7-1
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 Table 7-1, what is the probability that the sample mean differs from the population mean by more than 3 hours?

Question 51

TABLE 6-1
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 Table 6-1 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 52

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 53

TABLE 7-1
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 Table 7-1, what is the probability that the sample mean exceeds the population mean by more than 2 hours?

Question 54

TABLE 7-2
According to a survey, only 15% of customers who visited the website 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 Table 7-2, what proportion of the samples will have less than 15% of customers who will make a purchase after visiting the website?

Question 55

TABLE 7-1
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 Table 7-1, 90% of all the samples of 4 will have a sample mean of no more than how many hours from the population mean?

Question 56

The finite population correction factor is

A)
B)
C)
D)

Question 57

TABLE 7-2
According to a survey, only 15% of customers who visited the website 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 Table 7-2, the standard error of all the sample proportions of customers who will make a purchase after visiting the website is ________.

Question 58

TABLE 7-1
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 Table 7-1, 5% of all the samples of 4 will have a sample mean of at least how many hours above the population mean?

Question 59

TABLE 7-1
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 Table 7-1, what is the standard error of all the sample means?

Question 60

TABLE 7-1
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 Table 7-1, what is the probability that the sample mean differs from the population mean by less than 2 hours?

Question 61

TABLE 8-1
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 Table 8-1, 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.

Question 62

TABLE 7-2
According to a survey, only 15% of customers who visited the website 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 Table 7-2, 90% of the samples will have more than what percentage of customers who will make a purchase after visiting the website?

Question 63

TABLE 8-1
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 Table 8-1, there are 10 possible samples of 100 stores that can be selected out of the population of 1,000 stores.

Question 64

TABLE 8-1
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 Table 8-1, of all possible samples of 100 stores taken from the population of 1,000 stores, 95% of the confidence intervals developed will contain the true population mean within the interval.

Question 65

TABLE 8-1
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 Table 8-1, 95% of the stores have sold between 5.623 and 6.377 lawnmowers.

Question 66

TABLE 8-1
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 Table 8-1, 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 67

TABLE 8-1
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 Table 8-1, 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 68

TABLE 8-1
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 Table 8-1, we do not know for sure whether the true population mean is between 5.623 and 6.377 lawnmowers sold.

Question 69

TABLE 8-2
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 near 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 Table 8-2, what will be the 90% confidence interval for the mean market price of the houses in the suburban county constructed by the consulting group?

Question 70

TABLE 8-2
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 near 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 Table 8-2, if the investor wants a 95% confidence on estimating the true population mean market price of the houses in the suburban county to be within $10,000, how large a sample will he need?

Question 71

If we are performing a two-tail test of whether μ = 100, the probability of detecting a shift of the mean to 105 will be ________ the probability of detecting a shift of the mean to 110.

A) less than
B) greater than
C) equal to
D) not comparable to

Question 72

TABLE 8-2
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 near 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 Table 8-2, 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 73

For a given level of significance, if the sample size is increased but the summary statistics remain the same, the probability of committing a Type II error will increase.

Question 74

For a given level of significance, if the sample size is increased but the summary statistics remain the same, the probability of committing a Type I error will increase.

Question 75

For a given level of significance, if the sample size is increased but the summary statistics remain the same, the power of the test will increase.

Question 76

TABLE 9-1
A manufacturer produces light bulbs that have a mean life of at least 500 hours when the production process is working properly. Based on past experience, the population standard deviation is 50 hours and the light bulb life is normally distributed. The operations manager stops the production process if there is evidence that the population mean light bulb life is below 500 hours.
Referring to Table 9-1, if you select a sample of 100 light bulbs and are willing to have a level of significance of 0.10, the probability of a Type II error is ________ if the population mean bulb life is 490 hours.

Question 77

For a given sample size, the probability of committing a Type II error will increase when the probability of committing a Type I error is reduced.

Question 78

TABLE 8-2
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 near 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 Table 8-2, 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 79

TABLE 8-1
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 Table 8-1, 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

TABLE 8-2
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 near 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 Table 8-2, what will be the 90% confidence interval for the population proportion of houses that will be appraised for higher than the market prices?