Deck 5: Discrete Distributions

Question 1

The mean or the expected value of a discrete distribution is the long-run average of the occurrences.

Answer 1

True

Question 2

In a binomial experiment,any single trial contains only two possible outcomes and successive trials are dependent.

Answer 2

False

Question 3

Determine the mean,variance,and standard deviation of a discrete distribution.

Answer 3

The measures of central tendency and measures of variability discussed in Chapter 3 for grouped data can be applied to discrete distributions to compute a mean,a variance,and a standard deviation.Important examples of discrete distributions are the binomial distribution,the Poisson distribution,and the hypergeometric distribution.

Question 4

The assumption of independent trials in a binomial distribution is not a great concern if the sample size is smaller than 1/20^th of the population size.

Question 5

Both the Poisson and the binomial distributions are discrete distribution and both have a given number of trials.

Question 6

A variable that can take on values at any point over a given interval is called a discrete random variable.

Question 7

The Poisson distribution is a discrete distribution.

Question 8

In a binomial distribution,p,the probability of getting a successful outcome on any single trial,remains the same from one trial to another.

Question 9

For the Poisson distribution,the mean and the standard deviation are the same.

Question 10

The number of automobiles sold by a dealership in a day is an example of a discrete random variable.

Question 11

The Poisson distribution is best suited to describe occurrences of rare events in a situation where each occurrence is independent of the other occurrences.

Question 12

For a binomial distribution in which the probability of success p = 0.5,the variance is twice the mean.

Question 13

The amount of time a patient waits in a doctor's office is an example of a continuous random variable.

Question 14

A binomial distribution is better than a Poisson distribution to describe the occurrence of major oil spills in the Gulf of Saint Lawrence.

Question 15

Solve problems involving the hypergeometric distribution using the hypergeometric formula.

Question 16

To compute the variance of a discrete distribution,it is not necessary to know the mean of the distribution.

Question 17

Solve problems involving the binomial distribution using the binomial formula and the binomial table.

Question 18

Solve problems involving the Poisson distribution using the Poisson formula and the Poisson table.

Question 19

Variables which take on values only at certain points over a given interval are called continuous random variables.

Question 20

Define a random variable in order to differentiate between a discrete distribution and a continuous distribution.

Question 21

A market research team compiled the following discrete probability distribution for families residing in Randolph County.In this distribution x represents the number of evenings the family dines outside their home during a week. The standard deviation of x is ___.

A)1.00
B)2.00
C)0.80
D)0.89
E)1.09

Question 22

A market research team compiled the following discrete probability distribution.In this distribution x represents the number of automobiles owned by a family. The mean (average)value of x is ___.

A)1.0
B)1.5
C)2.0
D)2.5
E)3.0

Question 23

A hypergeometric distribution applies to experiments in which the trials represent sampling without replacement.

Question 24

If x has a binomial distribution with p = .5,then the distribution of x is ___.

A)skewed to the right
B)skewed to the left
C)symmetric
D)a Poisson distribution
E)a hypergeometric distribution

Question 25

A market research team compiled the following discrete probability distribution for families residing in Randolph County.In this distribution x represents the number of evenings the family dines outside their home during a week. The mean (average)value of x is ___.

A)1.0
B)1.5
C)2.0
D)2.5
E)3.0

Question 26

The following graph is a binomial distribution with n = 6: This graph reveals that ___.

A)p > 0.5
B)p = 1.0
C)p = 0
D)p < 0.5
E)p = 1.5

Question 27

The following graph is a binomial distribution with n = 6: This graph reveals that ___.

A)p > 0.5
B)p = 1.0
C)p = 0
D)p < 0.5
E)p = 1.5

Question 28

A market research team compiled the following discrete probability distribution.In this distribution x represents the number of automobiles owned by a family. The standard deviation of x is ___.

A)0.80
B)0.89
C)1.00
D)2.00
E)2.25

Question 29

As in a binomial distribution,successive trials of a hypergeometric distribution are independent.

Question 30

For the Poisson distribution,the mean and the variance are the same.

Question 31

Poisson distribution describes the occurrence of discrete events that may occur over a continuous interval of time or space.

Question 32

The number of defective parts in a lot of 25 parts is an example of ___.

A)a discrete random variable
B)a continuous random variable
C)the Poisson distribution
D)the normal distribution
E)a constant

Question 33

You are offered an investment opportunity.Its outcomes and probabilities are presented in the following table: Which of the following statements is true?

A)This distribution is skewed to the right.
B)This is a binomial distribution.
C)This distribution is symmetric.
D)This distribution is skewed to the left.
E)This is a Poisson distribution

Question 34

You are offered an investment opportunity.Its outcomes and probabilities are presented in the following table: The mean of this distribution is ___.

A)-$400
B)$0
C)$200
D)$400
E)$500

Question 35

If x is the number of successes in an independent series of 10 trials,then x has a ___ distribution.

A)hypergeometric
B)Poisson
C)normal
D)binomial
E)exponential

Question 36

A market research team compiled the following discrete probability distribution.In this distribution x represents the number of automobiles owned by a family. Which of the following statements is true?

A)This distribution is skewed to the right.
B)This is a binomial distribution.
C)This is a normal distribution.
D)This distribution is skewed to the left.
E)This distribution is bimodal.

Question 37

You are offered an investment opportunity.Its outcomes and probabilities are presented in the following table: The standard deviation of this distribution is ___.

A)-$400
B)$663
C)$800,000
D)$894
E)$2000

Question 38

As in a binomial distribution,each trial of a hypergeometric distribution results in one of two mutually exclusive outcomes,i.e. ,either a success or a failure.

Question 39

A Bernoulli process (each trial)has exactly ___ possible outcomes.

A)8
B)4
C)2
D)1
E)6

Question 40

The volume of liquid in an unopened 1-litre can of paint is an example of ___.

A)the binomial distribution
B)the normal distribution
C)a continuous random variable
D)a discrete random variable
E)a constant

Question 41

If x is a binomial random variable with n=8 and p=0.6,the mean value of x is ___.

A)6
B)4.8
C)3.2
D)8
E)48

Question 42

If x is a binomial random variable with n=8 and p=0.6,what is the probability that x is equal to 4?

A)0.500
B)0.005
C)0.124
D)0.232
E)0.578

Question 43

Pinky Bauer,Chief Financial Officer of Harrison Haulers,Inc. ,suspects irregularities in the payroll system,and orders an inspection of a random sample of vouchers issued since January 1,2013.A sample of ten vouchers is randomly selected,without replacement,from the population of 2,000 vouchers.Each voucher in the sample is examined for errors and the number of vouchers in the sample with errors is denoted by x.If 20% of the population of vouchers contain errors,P(x = 0)is ___.

A)0.8171
B)0.1074
C)0.8926
D)0.3020
E)0.2000

Question 44

A student randomly guesses the answers to a five question true/false test.If there is a 50% chance of guessing correctly on each question,what is the probability that the student misses exactly 1 question?

A)0.200
B)0.031
C)0.156
D)0.073
E)0.001

Question 45

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

Question 46

Pinky Bauer,Chief Financial Officer of Harrison Haulers,Inc. ,suspects irregularities in the payroll system,and orders an inspection of a random sample of vouchers issued since January 1,2013.A sample of ten vouchers is randomly selected,without replacement,from the population of 2,000 vouchers.Each voucher in the sample is examined for errors and the number of vouchers in the sample with errors is denoted by x.If 20% of the population of vouchers contain errors,P(x>0)is ___.

A)0.8171
B)0.1074
C)0.8926
D)0.3020
E)1.0000

Question 47

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 of non-authentic names in her sample,P(x=0)is ___.

A)0.8154
B)0.0467
C)0.0778
D)0.4000
E)0.5000

Question 48

A student randomly guesses the answers to a five question true/false test.If there is a 50% chance of guessing correctly on each question,what is the probability that the student misses no questions?

A)0.000
B)0.200
C)0.500
D)0.031
E)1.000

Question 49

The following graph is a binomial distribution with n = 6: This graph reveals that ___.

A)p = 0.5
B)p = 1.0
C)p = 0
D)p < 0.5
E)p = 1.5

Question 50

On Saturdays,cars arrive at Sam Schmitt's Scrub and Shine Car Wash 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

Question 51

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

Question 52

Pinky Bauer,Chief Financial Officer of Harrison Haulers,Inc. ,suspects irregularities in the payroll system,and orders an inspection of a random sample of vouchers issued since January 1,2013.A sample of ten vouchers is randomly selected,without replacement,from the population of 2,000 vouchers.Each voucher in the sample is examined for errors and the number of vouchers in the sample with errors is denoted by x.If 20% of the population of vouchers contains errors,the mean value of x is ___.

A)400
B)2
C)200
D)5
E)1

Question 53

If x is a binomial random variable with n=8 and p=0.6,the standard deviation of x is ___.

A)4.8
B)3.2
C)1.92
D)1.39
E)1.00

Question 54

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 of non-authentic names in her sample,P(x>0)is ___.

A)0.2172
B)0.9533
C)0.1846
D)0.9222
E)1.0000

Question 55

For the Poisson distribution of a random variable lambda (λ)is 5 occurrences per ten-minute time interval.If we want to analyze the number of occurrences per hour,we must use an adjusted value for lambda equal to ___.

A)5
B)60
C)30
D)10
E)20

Question 56

Pinky Bauer,Chief Financial Officer of Harrison Haulers,Inc. ,suspects irregularities in the payroll system,and orders an inspection of a random sample of vouchers issued since January 1,2013.A sample of ten vouchers is randomly selected,without replacement,from the population of 2,000 vouchers.Each voucher in the sample is examined for errors and the number of vouchers in the sample with errors is denoted by x.If 20% of the population of vouchers contains errors,the standard deviation of x is ___.

A)1.26
B)1.60
C)14.14
D)3.16
E)0.00

Question 57

A fair coin is tossed 5 times.What is the probability that exactly 2 heads are observed?

A)0.313
B)0.073
C)0.400
D)0.156
E)0.250

Question 58

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 of non-authentic names in her sample,P(x<2)is ___.

A)0.3370
B)0.9853
C)0.9785
D)0.2333
E)0.5000

Question 59

Twenty five items are sampled.Each of these has the same probability of being defective.The probability that exactly 2 of the 25 are defective could best be found by ___.

A)using the normal distribution
B)using the binomial distribution
C)using the Poisson distribution
D)using the exponential distribution
E)using the uniform distribution

Question 60

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

Question 61

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

A)Poisson distribution
B)Pascal distribution
C)binomial distribution
D)hypergeometric distribution
E)exponential distribution

Question 62

On Saturdays,cars arrive at Sami Schmitt's Scrub and Shine Car Wash 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

Question 63

One hundred policyholders file claims with CareFree Insurance.Ten of these claims are fraudulent.Claims manager Earl Evans randomly selects four of the ten claims for thorough investigation.If x represents the number of fraudulent claims in Earl's sample,x has a ___ distribution.

A)continuous
B)normal
C)binomial
D)hypergeometric
E)exponential

Question 64

Suppose a committee of 3 people is to be selected from a group consisting of 4 men and 5 women.What is the probability that all three people selected are men?

A)0.05
B)0.33
C)0.11
D)0.80
E)0.90

Question 65

Aluminum castings are processed in lots of five each.A sample of two castings is randomly selected from each lot for inspection.A particular lot contains one defective casting;and x is the number of defective castings in the sample.P(x=1)is ___.

A)0.2
B)0.4
C)0.6
D)0.8
E)1.0

Question 66

Suppose a committee of 3 people is to be selected from a group consisting of 4 men and 5 women.What is the probability that one man and two women are selected?

A)0.15
B)0.06
C)0.33
D)0.48
E)0.58

Question 67

Ten policyholders file claims with CareFree Insurance.Three of these claims are fraudulent.Claims manager Earl Evans randomly selects three of the ten claims for thorough investigation.If x represents the number of fraudulent claims in Earl's sample,P(x=0)is ___.

A)0.0083
B)0.3430
C)0.0000
D)0.2917
E)0.8917

Question 68

The probability of selecting 2 male employees and 3 female employees for promotions in a small company would best be modelled with the ___.

A)binomial distribution
B)hypergeometric distribution
C)Poisson distribution
D)hyperbinomial distribution
E)exponential distribution

Question 69

If sampling is performed without replacement,the hypergeometric distribution should be used.However,the binomial may be used to approximate this if ___.

A)n > 5%N
B)n < 5%N
C)the population size is very small
D)there are more than two possible outcomes of each trial
E)the outcomes are continuous

Question 70

The hypergeometric distribution is similar to the binomial distribution except that ___.

A)sampling is done with replacement in the hypergeometric
B)sampling is done without replacement in the hypergeometric
C)x does not represent the number of successes in the hypergeometric
D)there are more than two possible outcomes in the hypergeometric

Question 71

Aluminum castings are processed in lots of five each.A sample of two castings is randomly selected from each lot for inspection.A particular lot contains one defective casting;and x is the number of defective castings in the sample.P(x=0)is ___.

A)0.2
B)0.4
C)0.6
D)0.8
E)1.0

Question 72

Ten policyholders file claims with CareFree Insurance.Three of these claims are fraudulent.Claims manager Earl Evans randomly selects three of the ten claims for thorough investigation.If x represents the number of fraudulent claims in Earl's sample,P(x=1)is ___.

A)0.5250
B)0.4410
C)0.3000
D)0.6957
E)0.9957

Question 73

One hundred policyholders file claims with CareFree Insurance.Ten of these claims are fraudulent.Claims manager Earl Evans randomly selects four of the ten claims for thorough investigation.If x represents the number of fraudulent claims in Earl's sample,x has a ___.

A)normal distribution
B)hypergeometric distribution,but may be approximated by a binomial
C)binomial distribution,but may be approximated by a normal
D)binomial distribution,but may be approximated by a Poisson
E)exponential distribution

Question 74

Circuit boards for wireless telephones are etched in an acid bath,in batches of 100 boards.A sample of seven boards is randomly selected from each lot for inspection.A particular batch contains two defective boards;and x is the number of defective boards in the sample.P(x=0)is ___.

A)0.1315
B)0.8642
C)0.0042
D)0.6134
E)0.8134

Question 75

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

Question 76

The number of phone calls arriving at a switchboard in a 10 minute time period would best be modelled with the ___.

A)binomial distribution
B)hypergeometric distribution
C)Poisson distribution
D)hyperbinomial distribution
E)exponential distribution

Question 77

The probability of selecting 3 defective items and 7 good items from a warehouse containing 10 defective and 50 good items would best be modelled with the ___.

A)binomial distribution
B)hypergeometric distribution
C)Poisson distribution
D)hyperbinomial distribution
E)exponential distribution

Question 78

The Poisson distribution is being used to approximate a binomial distribution.If n=40 and p=0.06,what value of lambda would be used?

A)0.06
B)2.4
C)0.24
D)24
E)40

Question 79

Circuit boards for wireless telephones are etched in an acid bath,in batches of 100 boards.A sample of seven boards is randomly selected from each lot for inspection.A particular batch contains two defective boards;and x is the number of defective boards in the sample.P(x=2)is ___.

A)0.1315
B)0.8642
C)0.0042
D)0.6134
E)0.0034

Question 80

Circuit boards for wireless telephones are etched in an acid bath,in batches of 100 boards.A sample of seven boards is randomly selected from each lot for inspection.A batch contains two defective boards;and x is the number of defective boards in the sample.P(x=1)is ___.

A)0.1315
B)0.8642
C)0.0042
D)0.6134
E)0.6789