Deck 7: Discrete Probability 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

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

Answer 2

True

Question 3

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

Answer 3

False

Question 4

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 5

The manager of a home improvement store is studying the number of on-the-job-accidents recorded. The manager provided the following probability distribution for a particular month: The standard deviation of this distribution is ___.

A) 1.800
B) 1.345
C) 1.400
D) 4.000
E) 1.457

Question 6

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 7

In a binomial distribution, π, the probability of getting a successful outcome on any single trial, increases proportionately with every success.

Question 8

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 9

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

Question 10

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

Question 11

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

Question 12

The manager of a home improvement store is studying the number of on-the-job-accidents recorded. The manager provided the following probability distribution for a particular month: The mean of this distribution is ___.

A) 2.1
B) 3.0
C) 1.3
D) 5
E) <1

Question 13

A Poisson distribution is characterized by one parameter.

Question 14

The number of successes in a hypergeometric distribution is unknown.

Question 15

The probabilities that a student wins $50,000, $20,000 or $12,000 are 0.7, 0.2 and 0.1 respectively. The expected value of the random x = win is approximately.

A) $37,800.
B) $40,200.
C) -$37,800.
D) -$40,200.
E) 0.

Question 16

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

Question 17

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

Question 18

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

Question 19

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

Question 20

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

Question 21

The probability distribution for the daily demand of laptops at a local store is shown below. In this distribution, the random variable x is the daily demand of laptops: The mean (average) value of x is ___.

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

Question 22

At A-Life Corporation, managers begin at $35/hour until they reach $50/hour (salaries are always to the nearest dollar). If the variable x = hourly wage has a discrete uniform distribution, what is the mean wage for the managers?

A) $28.33
B) $35.00
C) $37.50
D) $42.50
E) $50.00

Question 23

The probability distribution for the daily demand of laptops at a local store is shown below. In this distribution, the random variable x is the daily demand of laptops: The standard deviation of x is ___.

A) 1.02
B) 0.89
C) 1.40
D) .506
E) .588

Question 24

At A-Life Corporation, managers begin at $35/hour until they reach $50/hour (salaries are always to the nearest dollar). If the variable x = hourly wage has a discrete uniform distribution, what is the standard deviation of x?

A) $7.50
B) $37.50
C) $42.50
D) $50.00
E) $56.25

Question 25

The distribution of the number grade one students per household in a rural community is shown below. In this distribution, the random variable x is the number grade one students per household: The mean (average) value of x is ___.

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

Question 26

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 27

The distribution of the number grade one students per household in a rural community is shown below. In this distribution, the random variable x is the number grade one students per household: The standard deviation of x is ___.

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

Question 28

For a discrete uniform distribution, if a = 4 and b = 5, what is P(x=10)?

A) 0.5
B) 1.0
C) 1.5
D) -0.5
E) -1.0

Question 29

For a discrete uniform distribution, if a = 4 and b = 5, what is standard deviation?

A) 0.17
B) 0.29
C) 0.50
D) 1.00
E) 1.5

Question 30

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

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

Question 31

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 32

The formula for the mean of a discrete uniform distribution is

A) .
B) .
C) .
D) .
E) .

Question 33

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

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

Question 34

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 35

At A-Life Corporation, managers begin at $35/hour until they reach $50/hour (salaries are always to the nearest dollar). If the variable x = hourly wage has a discrete uniform distribution, what is the probability that a manager's wage is between $42 and $45?

A) 0.50
B) 0.35
C) 0.30
D) 0.25
E) 0.13

Question 36

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

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

Question 37

If x has a binomial distribution with π =.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 38

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 39

For a discrete uniform distribution, if a = 4 and b = 5, what is the expected value?

A) 0.5
B) 4.5
C) 1.5
D) 9.0
E) 4.0

Question 40

The probability distribution for the daily demand of laptops at a local store is shown below. In this distribution, the random variable x is the daily demand of laptops: 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 41

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 42

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 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, 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 44

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 45

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 46

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

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

Question 47

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 48

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 49

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 50

Which of the following conditions is $\textbf{ not }$ 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 51

Suppose an interdisciplinary committee of 3 faculty members is to be selected from a group consisting of 4 business faculty and 5 engineering faculty members. The probability that one business faculty and two engineering faculty are selected is approximately ___.

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

Question 52

The probability of selecting 3 executive employees and 7 administrative employees to win a promotional trip a company with 10 executive and 50 administrative employees would best be modelled with the ___.

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

Question 53

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 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 contains errors, the standard deviation of x is ___.

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

Question 55

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 56

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 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 on non-authentic names in her sample, the expected (mean) value of x is ___.

A) 2.50
B) 2.00
C) 1.50
D) 1.25
E) 1.35

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>0) is ___.

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

Question 59

Suppose an interdisciplinary committee of 3 faculty members is to be selected from a group consisting of 4 business faculty and 5 engineering faculty members. The probability that all three faculty selected are all in business is approximately ___.

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

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 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 61

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 62

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) geometric distribution

Question 63

The Human Resource manager of a corporation documents the frequency with which employees call in sick. The Human Resource manager develops the following probability distribution for the number of time staff called in sick in a particular month:
Determine the expected value and the standard deviation of the probability distribution.

Question 64

The probability that a student will pass an exam on any trial is 0.7. What is the standard deviation of the number of trials needed to pass the exam?

A) 0.540
B) 0.548
C) 0.782
D) 0.880
E) 0.002

Question 65

A basketball player makes 80% of her free throws. Suppose this probability is the same for each free throw she attempts. What is probability that she makes more than 5 free throw attempts this season?

A) 0.32
B) 0.032
C) 0.0032
D) 0.00032
E) 0.000030

Question 66

A basketball player makes 80% of her free throws. Suppose this probability is the same for each free throw she attempts. The probability that she doesn't make a free throw until her fifth attempt this season is

A) 0.32768.
B) 0.08192.
C) 0.00128.
D) 0.00032.
E) 0.00004.

Question 67

Which of the following random variables is geometric?

A) the number of phone calls received in a one-hour period
B) the number of cards I need to deal from a deck of 52 cards that has been thoroughly shuffled so that at least one of the cards is a heart
C) the number of digits I will read beginning at a randomly selected starting point in a table of random digits until I find a 7
D) all of the above
E) none of the above

Question 68

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

Question 69

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 70

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 71

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 72

Suppose X has a geometric distribution with probability 0.3 of success on each observation. The probability that X is 4 is

A) 0.0081.
B) 0.0189.
C) 0.1029.
D) 0.2401.
E) 0.2409.

Question 73

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

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

Question 74

The probability that a student will pass an exam on any trial is 0.7. What is the expected number of trials needed to pass the exam?

A) 0.420
B) 0.428
C) 0.429
D) 1.420
E) 1.430

Question 75

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 76

The probability that a student will pass an exam on any trial is 0.7. What is the probability that he will pass on the first trial?

A) 0.7
B) 0.21
C) 0.06
D) 0.021
E) 1.00

Question 77

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 78

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 79

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 80

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