Deck 30: The Normal Approximation to the Binomial Distribution

Question 1

True or False: 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.

Answer 1

False

Question 2

True or False: 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 2

True

Question 3

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

Answer 3

False

Question 4

True or False: 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 5

TABLE 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 Table 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 6

True or False: 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 7

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

Question 8

TABLE 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 Table 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 9

TABLE 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 Table 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 10

True or False: 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 11

TABLE 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 Table 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 12

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

Question 13

True or False: 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 14

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

Question 15

True or False: 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 16

True or False: 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 17

True or False: 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

TABLE 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 Table 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 19

TABLE 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 Table 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 20

True or False: 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 21

TABLE 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 Table 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 22

TABLE 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 Table 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 23

TABLE 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 Table 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 24

The probability that a particular brand of smoke alarm will function properly and sound an alarm in the presence of smoke is 0.8.A batch of 100,000 such alarms was produced by independent production lines.Which of the following distributions would you use to figure out the probability that at least 90,000 of them will function properly in case of a fire?

A)Exponential distribution
B)Poisson distribution
C)Normal distribution
D)Uniform distribution

Question 25

Suppose that past history shows that 60% of college students prefer Coca-Cola.A sample of 10,000 students is to be selected.Which of the following distributions would you use to figure out the probability that at least half of them will prefer Coca-Cola?

A)Exponential distribution
B)Poisson distribution
C)Normal distribution
D)Uniform distribution

Question 26

TABLE 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 Table 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 27

TABLE 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 Table 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.