Deck 5: Discrete Distributions

Question 1

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

Answer 1

False

Question 2

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

Answer 2

True

Question 3

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

Answer 3

True

Question 4

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

Question 5

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

Question 6

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

Question 7

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

Question 8

The number of visitors to a website each day is an example of a discrete random variable

Question 9

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

Question 10

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

Question 11

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 12

A hypergeometric distribution applies to experiments in which the trials represent sampling with replacement.

Question 13

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

Question 14

The Poisson distribution is a continuous distribution which is very useful in solving waiting time problems

Question 15

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

Question 16

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 17

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

Question 18

For the Poisson distribution the mean represents twice the value of the standard deviation..

Question 19

A Poisson distribution is characterized by one parameter.

Question 20

The variance of a discrete distribution increases if we add a positive constant to each one of its value.

Question 21

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 22

The number of successes in a hypergeometric distribution is unknown

Question 23

A recent analysis of the number of rainy days per month found the following outcomes and probabilities. The mean of this distribution is _____________.

A) 2
B) 3
C) 4
D) 5
E) <1

Question 24

In a hypergeometric distribution the population,N,is finite and known.

Question 25

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 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

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 28

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 29

Twenty five individuals are randomly selected out of 100 shoppers leaving a local bedding store.Each shopper was asked if they made a purchase during their visit. Each of the shoppers has the same probability of answering 'yes' to having made a purchase.The probability that exactly four of the twenty-five shoppers made a purchase 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 30

If x is a binomial random variable with n=10 and p=0.8,the standard deviation of x is _________.

A) 8.0
B) 1.26
C) 1.60
D) 64.0
E) 10

Question 31

In American Roulette,there are two zeroes and 36 non-zero numbers (18 red and 18 black).If a player bets 1 unit on red,his chance of winning 1 unit is therefore 18/38 and his chance of losing 1 unit (or winning -1)is 20/38.Let x be the player profit per game.The mean (average)value of x is approximately_______________.

A) 0.0526
B) -0.0526
C) 1
D) -1
E) 0

Question 32

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 33

The number of finance majors within the School of Business 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 34

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 35

If x is a binomial random variable with n=10 and p=0.8,what is the probability that x is equal to 4?

A) )0055
B) )0063
C) )124
D) )232
E) )994

Question 36

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 37

If x is a binomial random variable with n=10 and p=0.8,the mean value of x is _____.

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

Question 38

The speed at which a jet plane can fly is an example of _________.

A) neither discrete nor continuous random variable
B) both discrete and continuous random variable
C) a continuous random variable
D) a discrete random variable
E) a constant

Question 39

A market research team compiled the following discrete probability distribution on the number of sodas the average adult drinks each day. In this distribution,x represents the number of sodas which an adult drinks. The mean (average)value of x is _______________.

A) 1.4
B) 1.75
C) 2.10
D) 2.55
E) 3.02

Question 40

The volume of liquid in an unopened 1-gallon can of paint is an example of _________.

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

Question 41

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 1,2006.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 42

It is known that screws produced by a certain company will be defective with probability .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) 0.0264
E) 0.2211

Question 43

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

Question 44

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 1,2006. 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 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

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

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 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 48

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 49

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 50

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 51

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

Question 52

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 53

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

Question 54

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 1,2006. 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 55

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) 0.1493
B) 0.3333
C) 0.3678
D) 0.1336
E) 0.03

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 1,2006. 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 57

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 58

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

Question 59

During a recent sporting event,a quarter is tossed to determine which team picks the starting side.Suppose the referee says the coin will be tossed 3 times and the best two out of three wins If team A calls 'heads',what is the probability that exactly two heads are observed in three tosses?

A) )313
B) )375
C) )625
D) )875
E) )500

Question 60

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 61

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 62

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 63

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

Question 64

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 65

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

Question 66

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

Question 67

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 faculty selected are men is approximately _______

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

Question 68

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 69

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

Question 70

One hundred policyholders file claims with CareFree Insurance. Ten of these claims are fraudulent. Claims manager Earl Evans randomly selects four of the one hundred 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 71

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

Question 72

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

Question 73

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

Question 74

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

Question 75

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 76

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 77

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 78

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

Question 79

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 80

One hundred policyholders file claims with CareFree Insurance. Ten of these claims are fraudulent. Claims manager Earl Evans randomly selects four of the one hundred 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