Question 1

The number of bags arriving on the baggage claim conveyor belt in a 3-minute time period would best be modeled with the _________.
A)binomial distribution
B)hypergeometric distribution
C)Poisson distribution
D)hyperbinomial distribution
E)exponential distribution

Accepted Answer

The Poisson distribution is most appropriate for modeling the number of events (in this case, bags arriving on a conveyor belt) occurring within a fixed interval of time, assuming these events happen independently of each other and at a constant average rate.

Question 2

The hypergeometric distribution must be used instead of the binomial distribution when ______
A)sampling is done with replacement
B)sampling is done without replacement
C)n≥5% N
D)both b and c
E)there are more than two possible outcomes

Accepted Answer

The hypergeometric distribution is used when sampling is done without replacement (B) and when the sample size is a significant portion of the population (C), typically n≥5% N.

Question 3

A large industrial firm allows a discount on any invoice that is paid within 30 days.Of all invoices, 10% receive the discount.In a company audit, 10 invoices are sampled at random.The probability that fewer than 3 of the 10 sampled invoices receive the discount is approximately_______________.
A)0.1937
B)0.057
C)0.001
D)0.3486
E)0.9298

Accepted Answer

The answer of A large industrial firm allows a discount...

Question 4

Dorothy Little purchased a mailing list of 2,000 names and addresses for her mail order business, but after scanning the list she doubts the authenticity of the list.She randomly selects five names from the list for validation.If 40% of the names on the list are non-authentic, and x is the number on non-authentic names in her sample, the expected (average)value of x is ______________.
A)2.50
B)2.00
C)1.50
D)1.25
E)1.35

Accepted Answer

The answer of Dorothy Little purchased a mailing list of...

Question 5

The Poisson distribution is being used to approximate a binomial distribution.If n=30 and p=0.03, what value of lambda would be used?
A)0.09
B)9.0
C)0.90
D)90
E)30

Accepted Answer

Lambda (λ) in a Poisson distribution is calculated as λ = n * p. Here, λ = 30 * 0.03 = 0.90.

Question 6

The number of cars arriving at a toll booth in five-minute intervals is Poisson distributed with a mean of 3 cars arriving in five-minute time intervals.The probability of 3 cars arriving over a five-minute interval is _______.
A)0.2700
B)0.0498
C)0.2240
D)0.0001
E)0.0020

Accepted Answer

The answer of The number of cars arriving at a...

Question 7

Suppose an interdisciplinary committee of 3 faculty members is to be selected from a group consisting of 4 men and 5 women.The probability that all three of the selected faculty are men is approximately _______
A)0.05
B)0.33
C)0.11
D)0.80
E)0.90

Accepted Answer

The answer of Suppose an interdisciplinary committee of 3 faculty...

Question 8

The probability of selecting 2 baseball players and 3 basketball players for an intermural competition at a small sports camp would best be modeled with the _______.
A)binomial distribution
B)hypergeometric distribution
C)Poisson distribution
D)hyperbinomial distribution
E)exponential distribution

Accepted Answer

The hypergeometric distribution is the best model for this scenario because it deals with selecting a specific number of successes (e.g., baseball and basketball players) from a finite population without replacement, which matches the description of selecting players for a competition from a small sports camp.

Question 9

On Monday mornings, customers arrive at the coffee shop drive thru at the rate of 6 cars per fifteen-minute interval.Using the Poisson distribution, the probability that five cars will arrive during the next five-minute interval is _____________.
A)0.1008
B)0.0361
C)0.1339
D)0.1606
E)0.3610

Accepted Answer

The average rate of arrival is 2 cars per five-minute interval (since 6 cars per fifteen minutes translates to 2 cars per five minutes). Using the Poisson distribution formula P(X=k) = (λ^k * e^(-λ)) / k!, where λ = 2 and k = 5, the probability is calculated as approximately 0.0361.

Question 10

The number of defects per 1,000 feet of extruded plastic pipe is best modeled with the ________________.
A)Poisson distribution
B)Pascal distribution
C)binomial distribution
D)hypergeometric distribution
E)exponential distribution

Accepted Answer

The Poisson distribution is best suited for modeling the number of defects per unit of measure (e.g., per 1,000 feet of extruded plastic pipe) when these events occur independently and the average rate (defects per unit) is known.

Question 11

On Monday mornings, customers arrive at the coffee shop drive thru at the rate of 6 cars per fifteen-minute interval.Using the Poisson distribution, the probability that five cars will arrive during the next fifteen-minute interval is _____________.
A)0.1008
B)0.0361
C)0.1339
D)0.1606
E)0.5000

Accepted Answer

The answer of On Monday mornings, customers arrive at the...

Question 12

In a certain communications system, there is an average of 1 transmission error per 10 seconds.Assume that the distribution of transmission errors is Poisson.The probability of 1 error in a period of one-half minute is approximately ________
A)0.1494
B)0.3333
C)0.3678
D)0.1336
E)0.03

Accepted Answer

The average rate of errors is 1 error per 10 seconds, which translates to 3 errors per 30 seconds (or half a minute). Using the Poisson probability formula P(X=k) = (λ^k * e^(-λ)) / k!, where λ is the average rate (3 in this case) and k is the number of errors (1), we calculate the probability of 1 error in 30 seconds. This results in approximately 0.1494.

Question 13

The number of cars arriving at a toll booth in five-minute intervals is Poisson distributed with a mean of 3 cars arriving in five-minute time intervals.The probability of 5 cars arriving over a five-minute interval is _______.
A)0.0940
B)0.0417
C)0.1500
D)0.1008
E)0.2890

Accepted Answer

The answer of The number of cars arriving at a...

Question 14

Assume that a random variable has a Poisson distribution with a mean of 5 occurrences per ten minutes.The number of occurrences per hour follows a Poisson distribution with λ equal to _________
A)5
B)60
C)30
D)10
E)20

Accepted Answer

The Poisson distribution parameter λ represents the average number of occurrences in a fixed interval of time. Given the mean is 5 occurrences per ten minutes, for an hour (which is six times ten minutes), the mean would be 6 * 5 = 30 occurrences per hour.

Question 15

A large industrial firm allows a discount on any invoice that is paid within 30 days.Of all invoices, 10% receive the discount.In a company audit, 15 invoices are sampled at random.The mean (average)value of the number of the 15 sampled invoices that receive discount is _______
A)1
B)3
C)1.5
D)2
E)10

Accepted Answer

The mean value of the number of invoices receiving a discount in a sample of 15 is calculated by multiplying the total number of invoices (15) by the probability of receiving a discount (10% or 0.1). This gives 15 * 0.1 = 1.5.

Question 16

The Poisson distribution is being used to approximate a binomial distribution.If n=60 and p=0.02, what value of lambda would be used?
A)0.02
B)12
C)0.12
D)1.2
E)120

Accepted Answer

Lambda (λ) in a Poisson distribution is calculated as λ = n * p. Here, n = 60 and p = 0.02, so λ = 60 * 0.02 = 1.2.

Question 17

Which of the following conditions is not a condition for the hypergeometric distribution?
A)the probability of success is the same on each trial
B)sampling is done without replacement
C)there are only two possible outcomes
D)trials are dependent
E)n < 5%N

Accepted Answer

The answer of Which of the following conditions is not...

Question 18

It is known that screws produced by a certain company will be defective with a probability of .01, independently of each other.The company sells the screws in packages of 25 and offers a money-back guarantee that at most, 1 of the 25 screws is defective.Using Poisson approximation for binomial distribution, the probability that the company must replace a package is approximately _________
A)0.01
B)0.1947
C)0.7788
D)0.0265
E)0.2211

Accepted Answer

The answer of It is known that screws produced by...

Question 19

Suppose an interdisciplinary committee of 3 faculty members is to be selected from a group consisting of 4 men and 5 women.The probability that one male faculty and two female faculty are selected is approximately ______
A)0.15
B)0.06
C)0.33
D)0.48
E)0.58

Accepted Answer

The total number of ways to select 3 faculty members from 9 people is C(9,3). The number of ways to select 1 man from 4 is C(4,1), and the number of ways to select 2 women from 5 is C(5,2). The probability is (C(4,1) * C(5,2)) / C(9,3) = (4 * 10) / 84 = 40/84 ≈ 0.48.

Question 20

The probability of selecting 3 female employees and 7 male employees to win a promotional trip a company with 10 female and 50 male employees would best be modeled with the _______.
A)binomial distribution
B)hypergeometric distribution
C)Poisson distribution
D)hyperbinomial distribution
E)exponential distribution

Accepted Answer

The hypergeometric distribution is used when we are selecting without replacement from a finite population divided into two groups, in this case, female and male employees. It is the appropriate model for calculating the probability of selecting a specific number of successes (female employees) and failures (male employees) from the groups without replacement.

Quiz 5: Discrete Distributions

The number of bags arriving on the baggage claim conveyor belt in a 3-minute time period would best be modeled with the _________.

The hypergeometric distribution must be used instead of the binomial distribution when ______

A large industrial firm allows a discount on any invoice that is paid within 30 days.Of all invoices, 10% receive the discount.In a company audit, 10 invoices are sampled at random.The probability that fewer than 3 of the 10 sampled invoices receive the discount is approximately_______________.

The Poisson distribution is being used to approximate a binomial distribution.If n=30 and p=0.03, what value of lambda would be used?

The number of cars arriving at a toll booth in five-minute intervals is Poisson distributed with a mean of 3 cars arriving in five-minute time intervals.The probability of 3 cars arriving over a five-minute interval is _______.

Suppose an interdisciplinary committee of 3 faculty members is to be selected from a group consisting of 4 men and 5 women.The probability that all three of the selected faculty are men is approximately _______

The probability of selecting 2 baseball players and 3 basketball players for an intermural competition at a small sports camp would best be modeled with the _______.

On Monday mornings, customers arrive at the coffee shop drive thru at the rate of 6 cars per fifteen-minute interval.Using the Poisson distribution, the probability that five cars will arrive during the next five-minute interval is _____________.

The number of defects per 1,000 feet of extruded plastic pipe is best modeled with the ________________.

On Monday mornings, customers arrive at the coffee shop drive thru at the rate of 6 cars per fifteen-minute interval.Using the Poisson distribution, the probability that five cars will arrive during the next fifteen-minute interval is _____________.

In a certain communications system, there is an average of 1 transmission error per 10 seconds.Assume that the distribution of transmission errors is Poisson.The probability of 1 error in a period of one-half minute is approximately ________

The number of cars arriving at a toll booth in five-minute intervals is Poisson distributed with a mean of 3 cars arriving in five-minute time intervals.The probability of 5 cars arriving over a five-minute interval is _______.

Assume that a random variable has a Poisson distribution with a mean of 5 occurrences per ten minutes.The number of occurrences per hour follows a Poisson distribution with λ equal to _________

A large industrial firm allows a discount on any invoice that is paid within 30 days.Of all invoices, 10% receive the discount.In a company audit, 15 invoices are sampled at random.The mean (average) value of the number of the 15 sampled invoices that receive discount is _______

The Poisson distribution is being used to approximate a binomial distribution.If n=60 and p=0.02, what value of lambda would be used?

Which of the following conditions is not a condition for the hypergeometric distribution?

Suppose an interdisciplinary committee of 3 faculty members is to be selected from a group consisting of 4 men and 5 women.The probability that one male faculty and two female faculty are selected is approximately ______

The probability of selecting 3 female employees and 7 male employees to win a promotional trip a company with 10 female and 50 male employees would best be modeled with the _______.