Deck 6: Discrete Probability Distributions

Question 1

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

Answer 1

A

Question 2

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

Answer 2

A

Question 3

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

Answer 3

A

Question 4

Identify Discrete Probability Distributions

Question 5

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 6

Construct Probability Histograms
The random variable x represents the number of boys in a family of three children. Assuming that boys and girls are equally likely, (a) construct a probability distribution, and (b) graph the probability histogram.

Question 7

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 8

Identify Discrete Probability Distributions

Question 9

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

Question 10

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 11

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

A) discrete
B) continuous

Question 12

Identify Discrete Probability Distributions

Question 13

Identify Discrete Probability Distributions
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.

Question 14

Identify Discrete Probability Distributions

Question 15

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 16

Classify the following random variable according to whether it is discrete or continuous
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 190 customers last Saturday morning and decided to observe their shopping habits. They recorded the number of items that each of the customers purchased as well as the total time the customers spent in the store. Identify the types of variables recorded by the 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 17

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 18

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 19

Classify the following random variable according to whether it is discrete or continuous
The number of violent crimes committed in a day possesses a distribution with a mean of 1.3 crimes per day and a standard deviation of four crimes per day. A random sample of 120 days was observed, and the sample mean number of crimes for the sample was calculated. The data that was collected in this experiment could be measured with a __________ random variable.

A) discrete
B) continuous

Question 20

Identify Discrete Probability Distributions

Question 21

Interpret the Mean of a Discrete Random Variable as an Expected Value

Question 22

Construct Probability Histograms
Suppose the mean cost of the rats turned out to be $13.63 per week. Interpret this value.

A) The average cost for all weekly rat purchases is $13.63.
B) Most of the weeks resulted in rat costs of $13.63.
C) The median cost for the distribution of rat costs is $13.63.
D) The rat cost that occurs more often than any other is $13.63.

Question 23

Interpret the Mean of a Discrete Random Variable as an Expected Value
The expected value of a discrete probability distribution may be negative.

Question 24

Construct Probability Histograms

Question 25

Interpret the Mean of a Discrete Random Variable as an Expected Value

Question 26

Interpret the Mean of a Discrete Random Variable as an Expected Value

Question 27

Construct Probability Histograms

Question 28

Construct Probability Histograms

Question 29

Interpret the Mean of a Discrete Random Variable as an Expected Value
On one busy holiday weekend, a national airline has many requests for standby flights at half of the usual one-way air fare. However, past experience has shown that these passengers have only about a 1 in 5 chance of getting on the standby flight. When they fail to get on a flight as a standby, their only other choice is to fly first class on the next flight out. Suppose that the usual one-way air fare to a certain city is $194 and the cost of flying first class is $520. Should a passenger who wishes to fly to this city opt to fly as a standby [Hint: Find the expected cost of the trip for a person flying standby.]

Question 30

Interpret the Mean of a Discrete Random Variable as an Expected Value

Question 31

Construct Probability Histograms

Question 32

Construct Probability Histograms

Question 33

Construct Probability Histograms

Question 34

Construct Probability Histograms

Question 35

Construct Probability Histograms

Question 36

Interpret the Mean of a Discrete Random Variable as an Expected Value

Question 37

Construct Probability Histograms

Question 38

Interpret the Mean of a Discrete Random Variable as an Expected Value

Question 39

Construct Probability Histograms

Question 40

Construct Probability Histograms

Question 41

Determine Whether a Probability Experiment is a Binomial Experiment
Decide whether the experiment is a binomial experiment. If it is not, explain why. You draw a marble 300 times from a bag with three colors of marbles. The random variable represents the color of marble that is drawn.

Question 42

Determine Whether a Probability Experiment is a Binomial Experiment
Decide whether the experiment is a binomial experiment. If it is not, explain why. Each week, a man attends a club meeting in which he has a 36% chance of meeting a new member. The random variable is the number of times he meets a new member in 92 weeks.

Question 43

Compute the Variance and Standard Deviation of a Discrete Random Variable
The owner of a farmer s market was interested in determining how many oranges a person buys when they buy oranges. He asked the cashiers over a weekend to count how many oranges a person bought when they bought oranges and record this number for analysis at a later time. The data is given below in the table. The random variable x represents the number of oranges purchased and P(x) represents the probability that a customer will buy x oranges. Determine the variance of the number of oranges purchased by a customer.

Question 44

Compute the Variance and Standard Deviation of a Discrete Random Variable

Question 45

Interpret the Mean of a Discrete Random Variable as an Expected Value
In the American version of the Game Roulette, a wheel has 18 black slots, 8 red slots and 2 green slots. All slots are the same size. In a carnival game, a person wagers $2 on the roll of two dice. A person can wager on either red or black. Green is reserved for the house. If a player wagers $5 on either red or black and that color comes up, 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 46

Determine Whether a Probability Experiment is a Binomial Experiment
Decide whether the experiment is a binomial experiment. If it is not, explain why. Survey 150 college students see whether they are enrolled as a new student. The random variable represents the number of students enrolled as new students.

Question 47

Determine Whether a Probability Experiment is a Binomial Experiment
Decide whether the experiment is a binomial experiment. If it is not, explain why. Each week, a gambler plays blackjack at the local casino. The random variable is the number of times per week the player wins.

Question 48

Compute the Variance and Standard Deviation of a Discrete Random Variable

Question 49

Compute the Variance and Standard Deviation of a Discrete Random Variable
A baseball player is asked to swing at pitches in sets of four. The player swings at 100 sets of 4 pitches. The probability distribution for hitting a particular number of pitches is given below. Determine the standard deviation for this discrete probability distribution.

Question 50

Compute the Variance and Standard Deviation of a Discrete Random Variable
A manager at a local company asked his employees how many times they had given blood in the last year. The results of the survey 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 the standard deviation for the number of times a person gave blood based on this survey

Question 51

Interpret the Mean of a Discrete Random Variable as an Expected Value
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 then the person gets $4 (the $2 wager and $2 winnings). If the total of the two dice is 8, 9, 10, 11, or 12 then the person gets nothing (loses $2). If the total of the two dice is 7, the person gets $0.75 back (loses $0.25). What is the expected value of playing the game once

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

Question 52

Compute the Variance and Standard Deviation of a Discrete Random Variable

Question 53

Determine Whether a Probability Experiment is a Binomial Experiment
Decide whether the experiment is a binomial experiment. If it is not, explain why. Testing a cough suppressant using 160 people to determine if it is effective. The random variable represents the number of people who find the cough suppressant to be effective.

Question 54

Compute the Variance and Standard Deviation of a Discrete Random Variable
A seed company has a test plot in which it is testing the germination of a hybrid seed. They plant 50 rows of 40 seeds per row. After a two-week period, the researchers count how many seed per row have sprouted. They noted that least number of seeds to germinate was 33 and some rows had all 40 germinate. The germination data is given below in the table. The random variable x represents the number of seed in a row that germinated 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.

Question 55

Determine Whether a Probability Experiment is a Binomial Experiment
Decide whether the experiment is a binomial experiment. If it is not, explain why. Survey 50 investors to see how many different stocks they own. The random variable represents the number of different stocks owned by each investor.

Question 56

Determine Whether a Probability Experiment is a Binomial Experiment
Decide whether the experiment is a binomial experiment. If it is not, explain why. You test four flu medicines. The random variable represents the flue medicine that is most effective.

Question 57

Compute the Variance and Standard Deviation of a Discrete Random Variable

Question 58

Determine Whether a Probability Experiment is a Binomial Experiment
Decide whether the experiment is a binomial experiment. If it is not, explain why. You observe the gender of the next 950 babies born at a local hospital. The random variable represents the number of boys.

Question 59

Compute the Variance and Standard Deviation of a Discrete Random Variable
The random variable x represents the number of girls in a family of three children. Assuming that boys and girls 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 60

Determine Whether a Probability Experiment is a Binomial Experiment
Decide whether the experiment is a binomial experiment. If it is not, explain why. In a game you spin a wheel that has 14 different letters 850 times. The random variable represents the selected letter on each spin of the wheel.

Question 61

Compute Probabilities of Binomial Experiments
The probability that a football game will go into overtime is 13%. What is the probability that two of three football games will go to into overtime

A) 0.044
B) 0.13
C) 0.295
D) 0.0169

Question 62

Compute Probabilities of Binomial Experiments
According to insurance records a car with a certain protection system will be recovered 95% of the time. Find the probability that 5 of 8 stolen cars will be recovered.

A) 0.005
B) 0.625
C) 0.95
D) 0.05

Question 63

Compute Probabilities of Binomial Experiments
A quiz consists of 10 multiple choice questions, each with five possible answers, one of which is correct. To pass the quiz a student must get 60% or better on the quiz. If a student randomly guesses, what is the probability that the student will pass the quiz

A) 0.006
B) 0.060
C) 0.377
D) 0.205

Question 64

Compute Probabilities of Binomial Experiments
In a recent survey, 70% of the community favored building a health center in their neighborhood. If 14 citizens are chosen, find the probability that exactly 6 of them favor the building of the health center.

A) 0.023
B) 0.126
C) 0.429
D) 0.700

Question 65

Compute Probabilities of Binomial Experiments
According to government data, the probability that an adult was never in a museum is 15%. In a random survey 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 66

Compute Probabilities of Binomial Experiments
According to the Federal Communications Commission, 70% of all U.S. households have vcrs. In a random sample 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 67

Compute Probabilities of Binomial Experiments
Fifty percent of the people that use the Internet order something online. Find the probability that only four of 8 Internet users will order something online.

A) 0.273
B) 0.500
C) 0.004
D) 4.375

Question 68

Determine Whether a Probability Experiment is a Binomial Experiment
If p is the probability of success of a binomial experiment, then the probability of failure is

Question 69

Compute Probabilities of Binomial Experiments
A recent survey found that 70% of all adults over 50 wear sunglasses for driving. In a random sample of 10 adults 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 70

Compute Probabilities of Binomial Experiments
Assume that male and female births are equally likely and that the birth of any child does not affect the probability 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 71

Compute Probabilities of Binomial Experiments
Sixty-five percent of men consider themselves knowledgeable soccer fans. If 14 men are randomly selected, find the probability that exactly four of them will consider themselves knowledgeable fans.

A) 0.005
B) 0.202
C) 0.65
D) 0.286

Question 72

Compute Probabilities of Binomial Experiments
Assume that male and female births are equally likely and that the birth of any child does not affect the probability 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 73

Compute Probabilities of Binomial Experiments
According to the Federal Communications Commission, 70% of all U.S. households have vcrs. In a random sample 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 74

Compute Probabilities of Binomial Experiments
According to government data, the probability that an adult was never in a museum is 15%. In a random survey 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 75

Compute Probabilities of Binomial Experiments
The probability that a house in an urban area will develop a leak is 5%. If 23 houses are randomly selected, what is the probability that none of the houses will develop a leak

A) 0.307
B) 0.050
C) 0.000
D) 0.002

Question 76

Compute Probabilities of Binomial Experiments
A quiz consists of 10 true or false questions. To pass the quiz a student must answer at least eight questions correctly. 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 77

Determine Whether a Probability Experiment is a Binomial Experiment
The trials of a binomial experiment must be mutually exclusive of each other.

Question 78

Determine Whether a Probability Experiment is a Binomial Experiment
Decide whether the experiment is a binomial experiment. If it is not, explain why. Selecting five cards, one at a time without replacement, from a standard deck of cards. The random variable is the number of picture cards obtained.

Question 79

Determine Whether a Probability Experiment is a Binomial Experiment
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 80

Compute Probabilities of Binomial Experiments
The probability that an individual has 20-20 vision is 0.15. In a class of 32 students, what is the probability of finding five people with 20-20 vision

A) 0.190
B) 0.156
C) 0.000
D) 0.15