Deck 6: Discrete Probability Distributions

Question 1

Consider the discrete probability distribution to the right when answering the following question. Find theprobability that x exceeds 4.

A) 0.39
B) 0.97
C) 0.61
D) 0.58

Answer 1

A

Question 2

Classify the following random variable according to whether it is discrete or continuous.
the number of emails received on any given day

A) discrete
B) continuous

Answer 2

A

Question 3

An Apple Pie Company knows that the number of pies sold each day varies from day to day. The ownerbelieves that on 50% of the days she sells 100 pies. On another 25% of the days she sells 150 pies, and she sells200 pies on the remaining 25% of the days. To make sure she has enough product, the owner bakes 200 pieseach day at a cost of $2 each. Assume any pies that go unsold are thrown out at the end of the day. If she sellsthe pies for $4 each, find the probability distribution for her daily profit.

Answer 3

A

Question 4

Classify the following random variable according to whether it is discrete or continuous.
the age of the oldest dog in a kennel

A) continuous
B) discrete

Question 5

Provide an appropriate response.
A random variable is

A) a numerical measure of the outcome of a probability experiment.
B) generated by a random number table.
C) the variable for which an algebraic equation is solved.
D) a qualitative attribute of a population.

Question 6

Provide an appropriate response.
The random variable x represents the number of credit cards that students have along with the correspondingprobabilities. Graph the probability histogram.

Question 7

Classify the following random variable according to whether it is discrete or continuous.
the number of pills in an aspirin bottle

A) discrete
B) continuous

Question 8

Classify the following random variable according to whether it is discrete or continuous.
the number of goals scored in a hockey game

A) discrete
B) continuous

Question 9

Classify the following random variable according to whether it is discrete or continuous.
the temperature in degrees Celsius on January 1st in Fargo, North Dakota

A) continuous
B) discrete

Question 10

Provide an appropriate response.
The peak shopping time at home improvement store is between 8:00am-11:00 am on Saturday mornings.Management at the home improvement store randomly selected 35 customers last Saturday morning anddecided to observe their shopping habits. They recorded the number of items that each of the customerspurchased as well as the total time the customers spent in the store. Identify the types of variables recorded bythe home improvement store.

A) number of items - discrete; total time - continuous
B) number of items - continuous; total time - continuous
C) number of items - continuous; total time - discrete
D) number of items - discrete; total time - discrete

Question 11

Classify the following random variable according to whether it is discrete or continuous.
the pressure of water coming out of a fire hose

A) continuous
B) discrete

Question 12

The sum of the probabilities of a discrete probability distribution must be

A) equal to one.
B) between zero and one.
C) greater than one.
D) less than or equal to zero. 3 Construct probability histograms.

Question 13

Provide an appropriate response.
The number of violent crimes committed in a day possesses a distribution with a mean of 1.8 crimes per dayand a standard deviation of four crimes per day. A random sample of 80 days was observed, and the samplemean number of crimes for the sample was calculated. The data that was collected in this experiment could bemeasured with a __________ random variable.

A) discrete
B) continuous

Question 14

Classify the following random variable according to whether it is discrete or continuous.
the cost of a road atlas

A) discrete
B) continuous

Question 15

Consider the discrete probability distribution to the right when answering the following question. Find theprobability that x equals 5.

A) 0.33
B) 0.67
C) 1.65
D) 3.35

Question 16

Classify the following random variable according to whether it is discrete or continuous.
the number of bottles of juice sold in a cafeteria during lunch

A) discrete
B) continuous

Question 17

Provide an appropriate response.
In an Italian cafe, the following probability distribution was obtained. The random variable x represents thenumber of toppings for a large pizza. Graph the probability histogram.

Question 18

Classify the following random variable according to whether it is discrete or continuous.
the speed of a car on a New York tollway during rush hour traffic

A) continuous
B) discrete

Question 19

Classify the following random variable according to whether it is discrete or continuous.
the heights of the bookcases in a school library

A) continuous
B) discrete

Question 20

Provide an appropriate response.
The random variable x represents the number of tests that a pet entering an animal shelter will have along withthe corresponding probabilities. Graph the probability histogram.

Question 21

In the American version of the Game Roulette, a wheel has 18 black slots, 8 red slots and 2 green slots. All slotsare the same size. In a carnival game, a person wagers $2 on the roll of two dice. A person can wager on eitherred or black. Green is reserved for the house. If a player wagers $5 on either red or black and that color comesup, they win $10 otherwise they lose their wager. What is the expected value of playing the game once?

A) -$0.26
B) -$0.50
C) $0.26
D) $0.50

Question 22

A legendary football coach was known for his winning seasons. He consistently won nine or more games perseason. Suppose x equals the number of games won up to the halfway mark (six games) in a 12-game season. Ifthis coach and his team had a probability p = 0.75 of winning any one game (and the winning or losing of onegame was independent of another), then the probability distribution of the number x of winning games in aseries of six games is: Find the expected number of winning games in the first half of the season for this coachʹs football teams.

Question 23

Provide an appropriate response.
Calculate the mean for the discrete probability distribution shown here.

Question 24

True or False: The expected value of a discrete probability distribution may be negative.

Question 25

Mamma Temte bakes six pies a day that cost $2 each to produce. On 15% of the days she sells only two pies. On30% of the days, she sells 4 pies, and on the remaining 55% of the days, she sells all six pies. If Mama Temtesells her pies for $6 each, what is her expected profit for a dayʹs worth of pies? [Assume that any leftover piesare given away.]

A) $16.80
B) $28.80
C) -$6.00
D) -$7.20

Question 26

In a carnival game, a person wagers $2 on the roll of two dice. If the total of the two dice is 2, 3, 4, 5, or 6 thenthe person gets $4 (the $2 wager and $2 winnings). If the total of the two dice is 8, 9, 10, 11, or 12 then theperson gets nothing (loses $2). If the total of the two dice is 7, the person gets $0.75 back (loses $0.25). What isthe expected value of playing the game once?

A) -$0.04
B) -$0.42
C) $2.00
D) $0.00

Question 27

An automobile insurance company estimates the following loss probabilities for the next year on a $25,000sports car: Assuming the company will sell only a $500 deductible policy for this model (i.e., the owner covers the first$500 damage), how much annual premium should the company charge in order to average $325 profit perpolicy sold?

Question 28

A dice game involves throwing three dice and betting on one of the six numbers that are on the dice. The gamecosts $6 to play, and you win if the number you bet appears on any of the dice. The distribution for theoutcomes of the game (including the profit) is shown below: Find your expected profit from playing this game.

A) -$0.77
B) $0.50
C) $6.18
D) $3.39

Question 29

A lab orders a shipment of 100 rats a week, 52 weeks a year, from a rat supplier for experiments that the labconducts. Prices for each weekly shipment of rats follow the distribution below: How much should the lab budget for next yearʹs rat orders assuming this distribution does not change. (Hint:find the expected price.)

A) $689.00
B) $13.25
C) $1325.00
D) $3,582,800.00

Question 30

Provide an appropriate response.
Use the frequency distribution to (a) construct a probability distribution for the random variable x whichrepresents the number of cars per family in a town of 1000 families, and (b) graph the probability histogram. 4

Question 31

The random variable x represents the number of girls in a family of three children. Assuming that boys andgirls are equally likely, find the mean and standard deviation for the random variable x.

A) mean: 1.50; standard deviation: 0.87
B) mean: 2.25; standard deviation: 0.87
C) mean: 1.50; standard deviation: 0.76
D) mean: 2.25; standard deviation: 0.76

Question 32

A seed company has a test plot in which it is testing the germination of a hybrid seed. They plant 50 rows of 40seeds per row. After a two-week period, the researchers count how many seed per row have sprouted. Theynoted that least number of seeds to germinate was 33 and some rows had all 40 germinate. The germinationdata is given below in the table. The random variable x represents the number of seed in a row thatgerminated and P(x) represents the probability of selecting a row with that number of seed germinating.Determine the mean number of seeds per row that germinated.

A) 36.9
B) 36.5
C) 36
D) 0.13

Question 33

A manager asked her employees how many times they had given blood in the last year. The results of thesurvey are given below. The random variable x represents the number of times a person gave blood and P(x)represents the probability of selecting an employee who had given blood that percent of the time. What is themean number of times a person gave blood based on this survey?

A) 1.6
B) 3.0
C) 2.0
D) 0.14

Question 34

Provide an appropriate response.
Calculate the mean for the discrete probability distribution shown here.

A) 8.93
B) 7
C) 28
D) 2.2325

Question 35

Provide an appropriate response.
A lab orders a shipment of 100 rats a week, 52 weeks a year, from a rat supplier for experiments that the labconducts. Prices for each weekly shipment of rats follow the distribution below: Suppose the mean cost of the rats turned out to be $13.00 per week. Interpret this value.

A) The average cost for all weekly rat purchases is $13.00.
B) Most of the weeks resulted in rat costs of $13.00.
C) The median cost for the distribution of rat costs is $13.00.
D) The rat cost that occurs more often than any other is $13.00.

Question 36

A random number generator is set to generate single digits between 0 and 9. One hundred and fifty randomnumbers are generated. The probability distribution for this random number generator is given below. Whatis the mean of this distribution?

A) 4.5
B) 6.6
C) 5
D) 7

Question 37

A baseball player is asked to swing at pitches in sets of four. The player swings at 100 sets of 4 pitches. Theprobability distribution for making a particular number of hits is given below. Determine the mean for thisdiscrete probability distribution.

A) 3
B) 4
C) 2
D) 3.5

Question 38

The produce manager at a farmerʹs market was interested in determining how many oranges a person buyswhen they buy oranges. He asked the cashiers over a weekend to count how many oranges a person boughtwhen they bought oranges and record this number for analysis at a later time. The data is given below in thetable. The random variable x represents the number of oranges purchased and P(x) represents the probabilitythat a customer will buy x apples. Determine the mean number of oranges purchased by a customer.

A) 3.97
B) 5.50
C) 3
D) 4

Question 39

A local bakery has determined a probability distribution for the number of cheesecakes that they sell in a givenday. The distribution is as follows: Find the number of cheesecakes that this local bakery expects to sell in a day.

A) 13.75
B) 13.82
C) 14.1
D) 10

Question 40

On one busy holiday weekend, a national airline has many requests for standby flights at half of the usualone-way air fare. However, past experience has shown that these passengers have only about a 1 in 5 chance ofgetting on the standby flight. When they fail to get on a flight as a standby, their only other choice is to fly firstclass on the next flight out. Suppose that the usual one-way air fare to a certain city is $142 and the cost offlying first class is $395. Should a passenger who wishes to fly to this city opt to fly as a standby? [Hint: Findthe expected cost of the trip for a person flying standby.]

Question 41

A seed company has a test plot in which it is testing the germination of a hybrid seed. They plant 50 rows of 40seeds per row. After a two-week period, the researchers count how many seed per row have sprouted. Theynoted that least number of seeds to germinate was 33 and some rows had all 40 germinate. The germinationdata is given below in the table. The random variable x represents the number of seed in a row thatgerminated and P(x) represents the probability of selecting a row with that number of seed germinating.Determine the standard deviation of the number of seeds per row that germinated.

A) 1.51
B) 7.13
C) 36.86
D) 6.07 6.2 The Binomial Probability Distribution
1 Determine whether a probability experiment is a binomial experiment.

Question 42

If p is the probability of success of a binomial experiment, then the probability of failure is 2 Compute probabilities of binomial experiments.

Question 43

A baseball player is asked to swing at pitches in sets of four. The player swings at 100 sets of 4 pitches. Theprobability distribution for hitting a particular number of pitches is given below. Determine the standarddeviation for this discrete probability distribution.

A) 1.05
B) 1.10
C) 1.21
D) 0.28

Question 44

Fifty percent of the people that use the Internet order something online. Find the probability that only five of 8Internet users will order something online.

A) 0.219
B) 0.625
C) 0.004
D) 1.750

Question 45

The random variable x represents the number of computers that families have along with the correspondingprobabilities. Find the mean and standard deviation for the random variable x.

A) mean: 1.18; standard deviation: 1.30
B) mean: 1.39; standard deviation: 0.64
C) mean: 1.39; standard deviation: 0.80
D) mean: 1.18; standard deviation: 0.64

Question 46

The probability that an individual has 20-20 vision is 0.17. In a class of 68 students, what is the probability offinding five people with 20-20 vision?

A) 0.012
B) 0.074
C) 0.000
D) 0.17

Question 47

Assume that male and female births are equally likely and that the birth of any child does not affect theprobability of the gender of any other children. Find the probability of exactly nine girls in ten births.

A) 0.010
B) 0.9
C) 0.020
D) 0.09

Question 48

Sixty-five percent of men consider themselves knowledgeable soccer fans. If 10 men are randomly selected,find the probability that exactly three of them will consider themselves knowledgeable fans.

A) 0.021
B) 0.252
C) 0.65
D) 0.300

Question 49

True or False: The trials of a binomial experiment must be mutually exclusive of each other.

Question 50

From the probability distribution, find the mean and standard deviation for the random variable x, whichrepresents the number of bicycles per household in a town of 1000 households.

Question 51

Assume that male and female births are equally likely and that the birth of any child does not affect theprobability of the gender of any other children. Find the probability of at most three girls in ten births.

A) 0.172
B) 0.300
C) 0.003
D) 0.333

Question 52

A manager at a local company asked his employees how many times they had given blood in the last year. Theresults of the survey are given below. The random variable x represents the number of times a person gaveblood and P(x) represents the probability of selecting an employee who had given blood that percent of thetime. What is the standard deviation for the number of times a person gave blood based on this survey?

A) 1.54
B) 1.82
C) 1.16
D) 2.23

Question 53

The probability that a house in an urban area will develop a leak is 4%. If 39 houses are randomly selected,what is the probability that none of the houses will develop a leak?

A) 0.204
B) 0.040
C) 0.000
D) 0.001

Question 54

In a recent survey, 72% of the community favored building a health center in their neighborhood. If 14 citizensare chosen, find the probability that exactly 10 of them favor the building of the health center.

A) 0.230
B) 0.001
C) 0.714
D) 0.720

Question 55

Which of the below is not a requirement for binomial experiment?

A) The trials are mutually exclusive.
B) The experiment is performed a fixed number of times.
C) For each trial there are two mutually exclusive outcomes.
D) The probability of success is fixed for each trial of the experiment.

Question 56

In a sandwich shop, the following probability distribution was obtained. The random variable x represents thenumber of condiments used for a hamburger. Find the mean and standard deviation for the random variable x.

A) mean: 1.14; standard deviation: 1.04
B) mean: 1.54; standard deviation: 1.30
C) mean: 1.30; standard deviation: 2.38
D) mean: 1.30; standard deviation: 1.54

Question 57

The owner of a farmerʹs market was interested in determining how many oranges a person buys when theybuy oranges. He asked the cashiers over a weekend to count how many oranges a person bought when theybought oranges and record this number for analysis at a later time. The data is given below in the table. Therandom variable x represents the number of oranges purchased and P(x) represents the probability that acustomer will buy x oranges. Determine the variance of the number of oranges purchased by a customer.

A) 3.57
B) 1.95
C) 3.97
D) 0.56

Question 58

The random variable x represents the number of tests that a patient entering a clinic will have along with thecorresponding probabilities. Find the mean and standard deviation for the random variable x.

A) mean: 1.59; standard deviation: 1.09
B) mean: 1.59; standard deviation: 3.72
C) mean: 2.52; standard deviation: 1.93
D) mean: 3.72; standard deviation: 2.52

Question 59

The probability that a football game will go into overtime is 15%. What is the probability that two of threefootball games will go to into overtime?

A) 0.057
B) 0.15
C) 0.325
D) 0.0225

Question 60

According to insurance records a car with a certain protection system will be recovered 87% of the time. Findthe probability that 4 of 10 stolen cars will be recovered.

A) 0.001
B) 0.400
C) 0.87
D) 0.13

Question 61

A quiz consists of 920 true or false questions. If the student guesses on each question, what is the mean numberof correct answers?

A) 460
B) 0
C) 920
D) 184

Question 62

A recent survey found that 69% of all adults over 50 wear sunglasses for driving. In a random sample of 20adults over 50, what is the mean and standard deviation of those that wear sunglasses?

A) mean: 13.8; standard deviation: 2.06833266
B) mean: 13.8; standard deviation: 3.71483512
C) mean: 6.2; standard deviation: 2.06833266
D) mean: 6.2; standard deviation: 3.71483512

Question 63

A history professor decides to give a 12-question true-false quiz. She wants to choose the passing grade suchthat the probability of passing a student who guesses on every question is less than 0.10. What score should beset as the lowest passing grade?

A) 9
B) 7
C) 10
D) 8

Question 64

According to government data, the probability that an adult was never in a museum is 15%. In a randomsurvey of 10 adults, what is the probability that two or fewer were never in a museum?

A) 0.820
B) 0.002
C) 0.800
D) 0.200

Question 65

According to insurance records, a car with a certain protection system will be recovered 92% of the time. If 800stolen cars are randomly selected, what is the mean and standard deviation of the number of cars recoveredafter being stolen?

A) mean: 736; standard deviation: 7.67333044
B) mean: 736; standard deviation: 58.88
C) mean: -5664: standard deviation: 7.67333044
D) mean: -5664: standard deviation: 58.88

Question 66

According to government data, the probability that an adult was never in a museum is 15%. In a randomsurvey of 10 adults, what is the probability that at least eight were in a museum?

A) 0.820
B) 0.200
C) 0.002
D) 0.800

Question 67

In a recent survey, 80% of the community favored building a health center in their neighborhood. If 15 citizensare chosen, what is the mean number favoring the health center?

A) 12
B) 15
C) 8
D) 10

Question 68

A quiz consists of 780 true or false questions. If the student guesses on each question, what is the standarddeviation of the number of correct answers?

A) 13.96424
B) 0
C) 2
D) 19.7484177

Question 69

We believe that 86% of the population of all Calculus I students consider calculus an exciting subject. Supposewe randomly and independently selected 29 students from the population. If the true percentage is really 86%,find the probability of observing 28 or more of the students who consider calculus to be an exciting subject inour sample of 29.

A) 0.072098
B) 0.012602
C) 0.059495
D) 0.927902

Question 70

A quiz consists of 10 true or false questions. To pass the quiz a student must answer at least eight questionscorrectly. If the student guesses on each question, what is the probability that the student will pass the quiz?

A) 0.055
B) 0.8
C) 0.20
D) 0.08

Question 71

A recent article in the paper claims that government ethics are at an all-time low. Reporting on a recent sample,the paper claims that 45% of all constituents believe their representative possesses low ethical standards.Suppose 20 of a representativeʹs constituents are randomly and independently sampled. Assuming the paperʹsclaim is correct, find the probability that more than eight but fewer than 12 of the 20 constituents sampledbelieve their representative possesses low ethical standards.

A) 0.454929
B) 0.295579
C) 0.689728
D) 0.889609 3 Compute the mean and standard deviation of a binomial random variable.

Question 72

A recent article in the paper claims that government ethics are at an all-time low. Reporting on a recent sample,the paper claims that 38% of all constituents believe their representative possesses low ethical standards.Assume that responses were randomly and independently collected. A representative of a district with 1,000people does not believe the paperʹs claim applies to her. If the claim is true, how many of the representativeʹsconstituents believe the representative possesses low ethical standards?

A) 380
B) 38
C) 620
D) 962

Question 73

A psychic network received telephone calls last year from over 1.5 million people. A recent article attempts toshed some light onto the credibility of the psychic network. One of the psychic networkʹs psychics agreed totake part in the following experiment. Five different cards are shuffled, and one is chosen at random. Thepsychic will then try to identify which card was drawn without seeing it. Assume that the experiment wasrepeated 50 times and that the results of any two experiments are independent of one another. If we assumethat the psychic is a fake (i.e., they are merely guessing at the cards and have no psychic powers), find theprobability that they guess at least three correctly.

A) 0.998715
B) 0.001257
C) 0.004371
D) 0.001093

Question 74

According to the Federal Communications Commission, 70% of all U.S. households have vcrs. In a randomsample of 15 households, what is the probability that at least 13 have vcrs?

A) 0.1268
B) 0.7
C) 0.8732
D) 0.5

Question 75

According to the Federal Communications Commission, 70% of all U.S. households have vcrs. In a randomsample of 15 households, what is the probability that the number of households with vcrs is between 10 and 12,inclusive?

A) 0.5947
B) 0.4053
C) 0.7
D) 0.2061

Question 76

Assume that male and female births are equally likely and that the birth of any child does not affect theprobability of the gender of any other children. Suppose that 200 couples each have a baby; find the mean andstandard deviation for the number of boys in the 200 babies.

Question 77

A recent survey found that 70% of all adults over 50 wear sunglasses for driving. In a random sample of 10adults over 50, what is the probability that at least six wear sunglasses?

A) 0.850
B) 0.700
C) 0.200
D) 0.006

Question 78

According to government data, the probability that an adult was never in a museum is 20%. In a randomsurvey of 70 adults, what is the mean and standard deviation of the number that were never in a museum?

A) mean: 14; standard deviation: 3.34664011
B) mean: 56 standard deviation: 3.74165739
C) mean: 56; standard deviation: 3.34664011
D) mean: 14; standard deviation: 3.74165739

Question 79

The probability that an individual has 20-20 vision is 0.1. In a class of 10 students, what is the mean andstandard deviation of the number with 20-20 vision in the class?

A) mean: 1; standard deviation: 0.9486833
B) mean: 10; standard deviation: 0.9486833
C) mean: 1; standard deviation: 1
D) mean: 10; standard deviation: 1

Question 80

The probability that a football game will go into overtime is 15%. In 260 randomly selected football games,what is the mean and the standard deviation of the number that went into overtime?

A) mean: 39; standard deviation: 5.75760367
B) mean: 39; standard deviation: 6.244998
C) mean: 36.4; standard deviation: 5.75760367
D) mean: 36.4; standard deviation: 6.244998