Deck 6: Discrete Probability Distributions

Question 1

A characteristic of a Bernoulli process is that the probability of success remains the same from one trial to the next.

Answer 1

True

Question 2

Approximately 84% of persons age 70 to 84 live in their own household and are income-qualified for home purchases.If four persons are randomly selected from this population,the probability that exactly two of the four live in their own household and are income-qualified is:

A) 0.8916
B) 0.4182
C) 0.0138
D) 0.5404
E) 0.1084

Answer 2

0.1084

Question 3

A characteristic of a Bernoulli process is that the trials are statistically dependent; that is,the outcome in any trial is affected by the outcomes of earlier trials,and it does affect the outcomes of later trials.

Answer 3

False

Question 4

The number of life insurance policy holders is an example of a discrete random variable.

Question 5

Theoretically,the number of times an event can occur over the given time span in a Poisson distribution has no limit.

Question 6

One characteristic of a discrete probability distribution is that values of x are exhaustive.

Question 7

A table,formula,or graph that shows all possible values a random variable can assume,together with their associated probabilities is referred to as:

A) Discrete probability distribution
B) Continuous probability distribution
C) Mixed probability distribution
D) Contaminated probability distribution

Question 8

For a Bernoulli process in which the number of trials is large and the probability of success on any given trial is very small,the Poisson distribution can be used as an approximation to the binomial distribution.

Question 9

The number of hungry people in Ethiopia is an example of a discrete random variable.

Question 10

The binomial distribution is best used to describe the number of customers arriving at a service point during a given period of time.

Question 11

The probability of success in a hypergeometric distribution does not remain constant from one trial to another.

Question 12

The binomial distribution requires that the probability of a success for each trial remains constant.

Question 13

Which of the following is not a characteristic of a discrete probability distribution?

A) The sum of the probabilities is one.
B) The values of x are exhaustive.
C) The value for the probability of any given x ranges from 0 to 1.
D) The values of x are mutually exclusive.
E) The sum of the probabilities for all possible values of x must be between 0 and 1.

Question 14

A new car salesperson knows that he sells cars to one customer out of 20 who enter the showroom.The probability that he will sell a car to exactly two of the next three customers is:

A) 0.9939
B) 0.0075
C) 0.0071
D) 0.0851
E) 0.1354

Question 15

The driving time between Big Rapids and Grand Rapids is an example of a discrete random variable.

Question 16

One characteristic of a discrete probability distribution is that the sum of the probabilities for all the possible values for x must be between 0 and 1.

Question 17

The hypergeometric distribution is similar to the binomial distribution in that successive trials are considered to be independent of one another.

Question 18

Which of the following most likely represents a discrete random variable?

A) Length of time between calls to an 800 number.
B) The number of years completed in the military services.
C) The S & P Industrial average of stock prices.
D) The amount of retail sales on a given day.
E) Length of time for which an apartment in a large complex remains vacant.

Question 19

Which of the following is a discrete random variable?

A) The average daily consumption of water in a U.S.household.
B) The weight of football players in the NFL.
C) The number of three-point shots completed in a college basketball game.
D) The time required to drive from Dallas to Denver.
E) The average daily temperature in the world.

Question 20

Theoretically,the number of successes in a binomial distribution has no limit.

Question 21

A survey of college students taking the professional exam to be certified as public school teachers shows that 15 percent fail.On a national exam day,12,000 students take the test.Let x denote the number who fail.The mean and standard deviation of the random variable x are,respectively:

A) 1800; 1530
B) 1800; 39.11
C) 10,200; 1530
D) 10,200; 39.11
E) 1200; 35.71

Question 22

The expected value,E(x),of a binomial probability distribution is:

A) $n + \pi$
B) $n \pi ( 1 - \pi )$
C) $n \pi$
D) $n + \pi - 1$

Question 23

Approximately 14 percent of the population of Arizona is 65 years or older.A random sample of five persons from this population is taken.The probability that less than 2 of the 5 are 65 years or older is:

A) 0.8533
B) 0.1467
C) 0.4704
D) 0.3829
E) None of these.

Question 24

A barbershop requires appointments for perms and hair cuts.Ten percent of those making appointments cancel or simply fail to show up.Next week's appointment calendar has 64 appointments.Let x be the number of missed appointments out of the 64.The probability that more than 3 cancellations and/or no-shows will occur during the next week is:

A) 0.3784
B) 0.8937
C) 0.7795
D) 0.9611
E) 0.1063

Question 25

Tornadoes for January in Kansas average 3.2 per month.The probability that in the next January at least 2 tornadoes will occur is:

A) 0.9592.
B) 0.0408.
C) 0.8288.
D) 0.1712.
E) none of these.

Question 26

Which of the following statements are true?

A) For the Poisson distribution= 3.2,the mean and standard deviation are both equal to 3.2.
B) For the Poisson distribution= 3.2,the mean and variance are both equal to 3.2.
C) For the Poisson distribution= 3.2,the mean is 3.2 and the standard deviation is 1.79.
D) Both B and C are correct.
E) All of these are correct.

Question 27

The variance of a binomial distribution for which n = 75 and = 0.20 is:

A) 375.
B) 75.
C) 15.
D) 12.

Question 28

Which probability distribution is appropriate when sampling is performed without replacement from a relatively small population?

A) Binomial distribution
B) Poisson distribution
C) Hypergeometric distribution
D) Normal distribution
E) Exponential distribution

Question 29

Tornadoes for January in Kansas average 3.2 per month.The probability that in the next January there will be between 1 and 3 tornadoes (inclusive)is:

A) 0.2087.
B) 0.5617.
C) 0.4383.
D) 0.4076.
E) 0.5924.

Question 30

NARRBEGIN: Police
A local police station receives an average 8.1 emergency telephone calls per hour.These calls are Poisson distributed.
The probability that the station will get five to seven calls in an hour is:

A) 0.5924.
B) 0.5617.
C) 0.4383.
D) 0.4076.
E) 0.3451.

Question 31

Which of the following is not a characteristic of the hypergeometric distribution?

A) The hypergeometric distribution is similar to the binomial distribution in focusing on the number of successes in a given number of consecutive trials.
B) The hypergeometric distribution is similar to the binomial distribution in the fact that the probability of success remains constant from one trail to the rest.
C) The hypergeometric distribution relies on sampling without replacement.
D) The hypergeometric distribution,the consecutive trials are not independent.
E) All of the above are characteristics of the hypergeometric distribution.

Question 32

A cashier at Carter's cafeteria can total an average of 2.2 trays per minute.The probability that the cashier will total exactly four trays in a minute is:

A) 0.9275.
B) 0.8918.
C) 0.1082.
D) 0.0992.
E) 0.1169.

Question 33

Brendalee and Mohammed go to a coffee shop during their lunch break and toss a coin to see who will pay.The probability that Brendalee will pay three days in a row is:

A) 0.2500
B) 0.5000
C) 0.1250
D) 0.0150
E) none of these.

Question 34

A cashier at Carter's cafeteria can total an average of 2.2 trays per minute.The probability that the cashier will total between four and ten trays in a minute is:

A) 0.9281.
B) 0.8193.
C) 0.1807.
D) 0.3772.
E) 0.0724.

Question 35

NARRBEGIN: Police
A local police station receives an average 8.1 emergency telephone calls per hour.These calls are Poisson distributed.
The probability that the station will get at least 4 calls in an hour is:

A) 0.0397.
B) 0.0941.
C) 0.9059.
D) 0.9603.
E) 0.9630.

Question 36

Tornadoes for January in Kansas average 3.2 per month.The probability that in the next January Kansas will experience exactly 2 tornadoes is:

A) 0.7913.
B) 0.4076.
C) 0.2087.
D) 0.1304.
E) 0.2226.

Question 37

The likelihood that someone who logs onto a particular site in a "shopping mall" on the Internet will purchase an item is 0.05 and follows the binomial distribution.If the site has 35 people accessing it in the next hour,what is the expected number of successes during this hour?

A) 1.75
B) 2.5
C) 0.05
D) 12
E) 35

Question 38

A Company manufactures women's hosiery.The company sells slightly irregular panty hose through a mail-order catalog service.If the company produces 300,000 pairs of hose per day and the probability of a pair not being irregular is 0.92,the average number that will be available for the catalog order department is:

A) 22080
B) 148.59
C) 24000
D) 154.92
E) 15.49

Question 39

NARRBEGIN: Police
A local police station receives an average 8.1 emergency telephone calls per hour.These calls are Poisson distributed.
The probability that the station will get nine calls in an hour is:

A) 0.1256.
B) 0.8744.
C) 0.0408.
D) 0.6918.
E) 0.3082.

Question 40

Which of the following is not a characteristic of a binomial experiment?

A) There is a sequence of identical trials.
B) Each trial results in two or more outcomes.
C) The trials are independent of each other.
D) Probability of success p is the same from one trial to another.

Question 41

NARRBEGIN: Egyptian
Let x represent the number of children in an Egyptian household.The probability distribution of x is as follows:
What is the probability that a randomly selected Egyptian household will have between 2 and 4 children?

Question 42

An urn contains 5 red marbles and 5 green ones.Two marbles are selected without replacement.What is the probability that both marbles are red?

Question 43

An urn contains 5 red marbles and 5 green ones.Two marbles are selected without replacement.What is the probability that at least one marble is red?

Question 44

Find the standard deviation of the number of children in an Egyptian household.

Question 45

NARRBEGIN: Egyptian
Let x represent the number of children in an Egyptian household.The probability distribution of x is as follows:
What is the probability that a randomly selected Egyptian household will have fewer than 4 children?

Question 46

Find the expected number of children in a randomly selected Egyptian household.

Question 47

A cashier at Carter's cafeteria can total an average of 2.2 trays per minute.The probability that the cashier will total no more than three trays in a minute is:

A) 0.1966.
B) 0.6227.
C) 0.9275.
D) 0.8193.

Question 48

The Poisson random variable is a:

A) discrete random variable with infinitely many possible values.
B) discrete random variable with finite number of possible values.
C) continuous random variable with infinitely many possible values.
D) continuous random variable with finite number of possible values.

Question 49

Which of the following events is best described using a hypergeometric distribution?

A) The number of customers entering a store during the next hour.
B) The number of accidents at a particular intersection during the next month.
C) The number of male jurors selected from a group of 25 individuals.
D) The number of correct responses in a multiple choice exam.
E) The number of heads after tossing a fair coin 10 times.

Question 50

As a rule of thumb,a binomial distribution for which the number of trials n is large can well be approximated by a Poisson distribution when the probability of success, $\pi$ ,is:

A) larger than 0.95.
B) larger than 0.50.
C) between 0.50 and 0.95.
D) smaller than .05.

Question 51

NARRBEGIN: MBI Co.
The MBI Company found that at the end of each month,2% of its two million accounting entries contained errors.Today,one operator has made 50 computer entries.
What is the probability that at most two errors were made?

Question 52

NARRBEGIN: Chocolates
A box of chocolates contains 18 pieces,10 of which have nuts while the remaining 8 do not.Four pieces are chosen at random.
What is the probability that exactly 2 pieces have nuts?

A) 0.412
B) 0.564
C) 0.681
D) 0.750
E) 0.833

Question 53

A high school play has five roles to fill with students.Seven girls and nine boys have expressed an interest in the play.What is the probability that exactly 0 girls will be selected?

Question 54

NARRBEGIN: Chocolates
A box of chocolates contains 18 pieces,10 of which have nuts while the remaining 8 do not.Four pieces are chosen at random.
What is the probability that at least 3 pieces have nuts?

A) 0.051
B) 0.118
C) 0.169
D) 0.242
E) 0.382

Question 55

A committee of eight politicians needs to be chosen from 11 Democrats and 15 Republicans.What is the probability that exactly 2 Democrats will be selected for the committee?

Question 56

A high school play has five roles to fill with students.Seven girls and nine boys have expressed an interest in the play.What is the probability that exactly 3 girls will be selected?

Question 57

The number of vacancies at a Gulf Shore resort motel on a day during weekends through the tourist season has the following probability distribution: If the mean is 2.07,compute the variance of this distribution.

Question 58

NARRBEGIN: Chocolates
A box of chocolates contains 18 pieces,10 of which have nuts while the remaining 8 do not.Four pieces are chosen at random.
What is the probability that no more than one piece has nuts?

A) 0.116
B) 0.206
C) 0.289
D) 0.444
E) 0.517

Question 59

NARRBEGIN: Egyptian
Let x represent the number of children in an Egyptian household.The probability distribution of x is as follows:
What is the probability that a randomly selected Egyptian household will have more than 2 children?

Question 60

A committee of eight politicians needs to be chosen from 11 Democrats and 15 Republicans.What is the probability that at least 5 Democrats will be selected for the committee?

Question 61

Ninety-five percent of the stockholders of an electric utility company own stock in other companies.If three stockholders are selected at random,what is the probability that exactly one has stock in another company?

Question 62

NARRBEGIN: Canoe club
A canoe club sponsor has taken canoeing groups through a particularly rough section of white water on a mountain river.Past trips and experience of the sponsor lead her to believe that fifty percent of the canoeists who attempt to paddle their way through this section will overturn.At the present time,there are five canoes approaching this treacherous section.Assume that the sponsor's estimate of the probability of a canoe overturning in this section of water is accurate.
What is the probability that three of the five canoes will capsize?

Question 63

A business office has purchased five new electric pencil sharpeners.The manufacturer of these pencil sharpeners states that twenty in one hundred of their sharpeners will require some maintenance or repair work during the first year's use.Find the probability that at least 3 of these sharpeners will need repair during the first year.

Question 64

NARRBEGIN: Chamber of Commerce
A local chamber of commerce is backing a plan for a new convention center.The chamber states that 60 percent of the voters favor the plan,which would raise tourism business and taxes for the residents.Four of the registered voters in the community are called at random.X is the number of voters called who say they favor the plan.
Find the probability that no one says they favor the plan.

Question 65

NARRBEGIN: Canoe club
A canoe club sponsor has taken canoeing groups through a particularly rough section of white water on a mountain river.Past trips and experience of the sponsor lead her to believe that fifty percent of the canoeists who attempt to paddle their way through this section will overturn.At the present time,there are five canoes approaching this treacherous section.Assume that the sponsor's estimate of the probability of a canoe overturning in this section of water is accurate.
What is the probability that only one of the five canoes will capsize?

Question 66

An attorney representing a client in an injury suit surveys the jury panel and finds that 30% of the potential jurors have experienced some type of job related injury.The attorney is hopeful that he will have six of the twelve jurors from this group.What is the probability that at least 6 jurors will have experienced a job-related injury?

Question 67

NARRBEGIN: Stockholders
The listed occupations of stockholders of a regional electric utility company included 9 percent who were homemakers.Six of these stockholders are randomly selected.
What is the probability that no stockholders are homemakers?

Question 68

NARRBEGIN: New York City
New York City is estimated to have 21 percent of the homes with T.V.sets served by cable T.V.If a random sample of four is taken from these homes find the probability distribution of x where x is the number of T.V.homes in the sample having cable T.V.
What is the probability that all four T.V.homes in the sample are served by cable?

Question 69

NARRBEGIN: Stockholders
The listed occupations of stockholders of a regional electric utility company included 9 percent who were homemakers.Six of these stockholders are randomly selected.
What is the probability that at least one is a homemaker?

Question 70

NARRBEGIN: Stockholders
The listed occupations of stockholders of a regional electric utility company included 9 percent who were homemakers.Six of these stockholders are randomly selected.
What is the probability that exactly three are homemakers?

Question 71

NARRBEGIN: New York City
New York City is estimated to have 21 percent of the homes with T.V.sets served by cable T.V.If a random sample of four is taken from these homes find the probability distribution of x where x is the number of T.V.homes in the sample having cable T.V.
What is the probability that at least one T.V.home in the sample is served by cable?

Question 72

NARRBEGIN: Canoe club
A canoe club sponsor has taken canoeing groups through a particularly rough section of white water on a mountain river.Past trips and experience of the sponsor lead her to believe that fifty percent of the canoeists who attempt to paddle their way through this section will overturn.At the present time,there are five canoes approaching this treacherous section.Assume that the sponsor's estimate of the probability of a canoe overturning in this section of water is accurate.
What is the probability that two of the five canoes will capsize?

Question 73

A fast food hamburger restaurant manager is interviewing high school persons age sixteen for possible employment.Persons age sixteen who apply for jobs in the area have no prior work-for-pay experience ninety percent of the time.Let x be the number of the four high school persons age sixteen who have no prior work-for-pay experience.If the manager plans to hire four,what is the probability that two of the four will have work experience?

Question 74

NARRBEGIN: Chamber of Commerce
A local chamber of commerce is backing a plan for a new convention center.The chamber states that 60 percent of the voters favor the plan,which would raise tourism business and taxes for the residents.Four of the registered voters in the community are called at random.X is the number of voters called who say they favor the plan.
Find the probability that exactly 2 voters sampled favor the plan.

Question 75

Twenty percent of the automobiles inspected at a state inspection station required repairs to meet the inspection standard.Three drivers arrive for auto inspections.Let x be the number of automobiles requiring repairs and find the probability that all three automobiles will require repair.

Question 76

NARRBEGIN: Appliance store
A small appliance store has 10 VCR's in stock.Four of the VCR's were damaged in shipment.The owner of the store gives his daughter and his son each a VCR for a birthday present.
What is the probability that both the gift VCR's will be defective?

Question 77

NARRBEGIN: Canoe club
A canoe club sponsor has taken canoeing groups through a particularly rough section of white water on a mountain river.Past trips and experience of the sponsor lead her to believe that fifty percent of the canoeists who attempt to paddle their way through this section will overturn.At the present time,there are five canoes approaching this treacherous section.Assume that the sponsor's estimate of the probability of a canoe overturning in this section of water is accurate.
What is the probability that none of the five canoes will capsize?

Question 78

NARRBEGIN: Canoe club
A canoe club sponsor has taken canoeing groups through a particularly rough section of white water on a mountain river.Past trips and experience of the sponsor lead her to believe that fifty percent of the canoeists who attempt to paddle their way through this section will overturn.At the present time,there are five canoes approaching this treacherous section.Assume that the sponsor's estimate of the probability of a canoe overturning in this section of water is accurate.
What is the probability that four of the five canoes will capsize?

Question 79

In an intermediate level economics class there are 18 students.Nine of these are economics majors.For class discussion purposes three students are randomly selected.What is the probability that at least one is an economics major?

Question 80

NARRBEGIN: Motor Co.
A Motor Company has purchased steel parts from a supplier for several years and has found that 10% of the parts must be returned because they are defective.An order of 25 parts is received.
What is the probability that no more than three of these parts are defective?