Deck 4: Discrete Probability Distributions

Question 1

A student has five motor vehicle accidents in one year and claims that having five accidents is not unusual.
Use the frequency distribution below to determine if the student is correct.

Answer 1

The student is not correct. For a student to have five accidents is unusual because the probability of this event is 0.026.

Question 2

State whether the variable is discrete or continuous. The blood pressures of a group of students the day before their final exam

A)continuous
B)discrete

Answer 2

continuous

Question 3

State whether the variable is discrete or continuous. The number of pills in a container of vitamins

A)discrete
B)continuous

Answer 3

discrete

Question 4

State whether the variable is discrete or continuous. The number of cups of coffee sold in a cafeteria during lunch

A)discrete
B)continuous

Question 5

State whether the variable is discrete or continuous. The number of phone calls to the attendance office of a high school on any given school day

A)discrete
B)continuous

Question 6

The random variable x represents the number of cars per household in a town of 1000 households. Find the probability of randomly selecting a household that has at least one car. $$\begin{array} { c | c } \text { Cars } & \text { Households } \\\hline 0 & 125 \\1 & 428 \\2 & 256 \\3 & 108 \\4 & 83\end{array}$$

A)0.875
B)0.125
C)0.500
D)0.083

Question 7

A sports analyst records the winners of NASCAR Winston Cup races for a recent season. The random variable
x represents the races won by a driver in one season. Use the frequency distribution to construct a probability
distribution.

Question 8

A sports announcer researched the performance of baseball players in the World Series. The random variable x
represents the number of of hits a player had in the series. Use the frequency distribution to construct a
probability distribution.

Question 9

State whether the variable is discrete or continuous. The age of the oldest student in a statistics class

A)continuous
B)discrete

Question 10

An insurance actuary asked a sample of senior citizens the cause of their automobile accidents over a two -year
period. The random variable x represents the number of accidents caused by their failure to yield the right of
way. Use the frequency distribution to construct a probability distribution.

Question 11

State whether the variable is discrete or continuous. The speed of a car on a Los Angeles freeway during rush hour traffic

A)continuous
B)discrete

Question 12

A baseball player gets four hits during the World Series and a sports announcer claims that getting four or
more hits is not unusual. Use the frequency distribution below to determine if the sports announcer is correct.

Question 13

State whether the variable is discrete or continuous. The cost of a Statistics textbook

A)discrete
B)continuous

Question 14

State whether the variable is discrete or continuous. The temperature in degrees Fahrenheit on July 4th in Juneau, Alaska

A)continuous
B)discrete

Question 15

Determine whether the number line represents a discrete random variable or a continuous random variable. Explain your reasoning.
The attendance at games for a sports team

A)Discrete; Attendance is a random variable that is countable.
B)Continuous; Attendance is a random variable that must be measured.

Question 16

State whether the variable is discrete or continuous. The height of a player on a basketball team

A)continuous
B)discrete

Question 17

The random variable x represents the number of cars per household in a town of 1000 households. Find the probability of randomly selecting a household that has between one and three cars, inclusive. $$\begin{array} { c | c } \text { Cars } & \text { Households } \\\hline 0 & 125 \\1 & 428 \\2 & 256 \\3 & 108 \\4 & 83\end{array}$$

A)0.792
B)0.125
C)0.208
D)0.256

Question 18

Determine whether the number line represents a discrete random variable or a continuous random variable. Explain your reasoning.
The length of time college students study each week

A)Continuous; Time is a random variable that must be measured.
B)Discrete; Time is a random variable that is countable.

Question 19

The random variable x represents the number of cars per household in a town of 1000 households. Find the probability of randomly selecting a household that has less than two cars. $$\begin{array} { c | c } \text { Cars } & \text { Households } \\\hline 0 & 125 \\1 & 428 \\2 & 256 \\3 & 108 \\4 & 83\end{array}$$

A)0.553
B)0.809
C)0.428
D)0.125

Question 20

State whether the variable is discrete or continuous. The number of goals scored in a soccer game

A)discrete
B)continuous

Question 21

One thousand tickets are sold at $2 each. One ticket will be randomly selected and the winner will receive a color television valued at $387. What is the expected value for a person that buys one ticket?

A)-$1.61
B)$1.61
C)$1.00
D)-$1.00

Question 22

Determine the probability distribution?s missing value. The probability that a tutor sees 0, 1, 2, 3, or 4 students on a given day. $$\begin{array} { l | c | c | c | c | c } \mathrm { x } & 0 & 1 & 2 & 3 & 4 \\\hline \mathrm { P } ( \mathrm { x } ) & ? & 0.15 & 0.20 & 0.20 & 0.25\end{array}$$

A)0.20
B)0.50
C)0.80
D)1.0

Question 23

In a pizza takeout restaurant, the following probability distribution was obtained. The random variable x represents the number of toppings for a large pizza. Find the mean and standard deviation. $$\begin{array} { c | c } \mathrm { x } & \mathrm { P } ( \mathrm { x } ) \\\hline 0 & 0.30 \\1 & 0.40 \\2 & 0.20 \\3 & 0.06 \\4 & 0.04\end{array}$$

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 24

Determine whether the distribution represents a probability distribution. If not, identify any requirements that
are not satisfied.

Question 25

Use the frequency distribution to (a)construct a probability distribution for the random variable x which
represents the number of cars per household in a town of 1000 households, and (b)graph the distribution.

Question 26

The random variable x represents the number of credit cards that adults have along with the corresponding
probabilities. Graph the probability distribution.

Question 27

Determine whether the distribution represents a probability distribution. If not, identify any requirements that
are not satisfied.

Question 28

If a person rolls doubles when tossing two dice, the roller profits $100. If the game is fair, how much should the person pay to play the game?

A)$20
B)$100
C)$99
D)$97

Question 29

Determine whether the distribution represents a probability distribution. If not, identify any requirements that
are not satisfied.

Question 30

Determine whether the distribution represents a probability distribution. If not, identify any requirements that
are not satisfied.

Question 31

In a pizza takeout restaurant, the following probability distribution was obtained. The random variable x
represents the number of toppings for a large pizza. Graph the probability distribution.

Question 32

The random variable x represents the number of boys 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 33

The random variable x represents the number of tests that a patient entering a hospital will have along with the corresponding probabilities. Find the mean and standard deviation. $$\begin{array} { l | c | c | c | c | c } \mathrm { x } & 0 & 1 & 2 & 3 & 4 \\\hline \mathrm { P } ( \mathrm { x } ) & \frac { 3 } { 17 } & \frac { 5 } { 17 } & \frac { 6 } { 17 } & \frac { 2 } { 17 } & \frac { 1 } { 17 }\end{array}$$

A)mean: 1.59; standard deviation: 1.09
B)mean: 1.59; standard deviation: 3.71
C)mean: 2.52; standard deviation: 1.93
D)mean: 3.72; standard deviation: 2.52

Question 34

At a raffle, 10,000 tickets are sold at $5 each for three prizes valued at $4,800, $1,200, and $400. What is the expected value of one ticket?

A)-$4.36
B)$4.36
C)$0.64
D)-$0.64

Question 35

At a raffle, 10,000 tickets are sold at $10 each for three prizes valued at $4,800, $1,200, and $400. What is the expected value of one ticket?

A)-$9.36
B)$9.36
C)-$0.64
D)$0.64

Question 36

The random variable x represents the number of tests that a patient entering a hospital will have along with the
corresponding probabilities. Graph the probability distribution.

Question 37

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 distribution.

Question 38

Determine whether the distribution represents a probability distribution. If not, identify any requirements that
are not satisfied.

Question 39

The random variable x represents the number of credit cards that adults have along with the corresponding probabilities. Find the mean and standard deviation. $$\begin{array} { c | c } \mathrm { x } & \mathrm { P } ( \mathrm { x } ) \\\hline 0 & 0.07 \\1 & 0.68 \\2 & 0.21 \\3 & 0.03 \\4 & 0.01\end{array}$$

A)mean: 1.23; standard deviation: 0.66
B)mean: 1.30; standard deviation: 0.32
C)mean: 1.30; standard deviation: 0.44
D)mean: 1.23; standard deviation: 0.44

Question 40

Determine the probability distribution?s missing value. The probability that a tutor will see 0, 1, 2, 3, or 4 students $$\begin{array} { l | c | c | c | c | c } \mathrm { x } & 0 & 1 & 2 & 3 & 4 \\\hline \mathrm { P } ( \mathrm { x } ) & 0.16 & 0.04 & 0.19 & 0.14 & ?\end{array}$$

A)0.47
B)0.8
C)0.53
D)-0.67

Question 41

Find the standard deviation of the binomial distribution for which n = 1000 and p = 0.94.

A)7.51
B)56.4
C)940
D)6.31

Question 42

Decide whether the experiment is a binomial experiment. If it is not, explain why. Testing a pain reliever using
740 people to determine if it is effective. The random variable represents the number of people who find the
pain reliever to be effective.

Question 43

Decide whether the experiment is a binomial experiment. If it is not, explain why. You roll a die 100 times. The
random variable represents the number that appears on each roll of the die.

Question 44

Decide whether the experiment is a binomial experiment. If it is not, explain why. Surveying 600 prisoners to
see whether they are serving time for their first offense. The random variable represents the number of
prisoners serving time for their first offense.

Question 45

Decide whether the experiment is a binomial experiment. If it is not, explain why. You test four pain relievers.
The random variable represents the pain reliever that is most effective.

Question 46

Find the mean of the binomial distribution for which n = 40 and p = 0.2.

A)8
B)2.53
C)20
D)40

Question 47

Decide whether the experiment is a binomial experiment. If it is not, explain why. Surveying 250 prisoners to
see how many crimes in which they were convicted. The random variable represents the number of crimes in
which each prisoner was convicted.

Question 48

Decide whether the experiment is a binomial experiment. If it is not, explain why. You observe the gender of
the next 250 babies born at a local hospital. The random variable represents the number of girls.

Question 49

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

Question 50

Decide whether the experiment is a binomial experiment. If it is not, explain why. Each week, a man plays a
game in which he has a 39% chance of winning. The random variable is the number of times he wins in 51
weeks.

Question 51

Decide whether the experiment is a binomial experiment. If it is not, explain why. You spin a number wheel
that has 19 numbers 450 times. The random variable represents the winning numbers on each spin of the
wheel.

Question 52

In a recent survey, 80% of the community favored building a police substation in their neighborhood. If 15 citizens are chosen, what is the mean number favoring the substation?

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

Question 53

In a recent survey, 80% of the community favored building a police substation in their neighborhood. If 15 citizens are chosen, what is the standard deviation of the number favoring the substation?

A)1.55
B)2.40
C)0.98
D)0.55

Question 54

In one city, 24% of adults smoke. In groups of size 130 of adults, what is the variance of the number that smoke ?

A)23.71
B)4.87
C)31.2
D)11.86

Question 55

In a raffle, 1,000 tickets are sold for $2 each. One ticket will be randomly selected and the winner will receive a laptop computer valued at $1200. What is the expected value for a person that buys one ticket?

A)-$0.80
B)$0.8
C)$1.20
D)-$1.20

Question 56

A test consists of 700 true or false questions. If the student guesses on each question, what is the mean number of correct answers?

A)350
B)0
C)700
D)140

Question 57

Find the variance of the binomial distribution for which n = 800 and p = 0.87.

A)90.48
B)9.51
C)696
D)32.54

Question 58

The probability that a house in an urban area will be burglarized is 5%. If 20 houses are randomly selected, what is the mean of the number of houses burglarized?

A)1
B)10
C)0.5
D)1.5

Question 59

A test consists of 800 true or false questions. If the student guesses on each question, what is the standard deviation of the number of correct answers?

A)14.14
B)0
C)2
D)20

Question 60

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 red cards
obtained.

Question 61

The probability that an individual is left-handed is 0.12. In a class of 39 students, what is the probability of finding five left-handers?

A)0.186
B)0.128
C)0.000
D)0.12

Question 62

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

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

Question 63

In a recent survey, 64% of the community favored building a police substation in their neighborhood. If 14 citizens are chosen, find the probability that exactly 8 of them favor the building of the police substation.

A)0.184
B)0.058
C)0.571
D)0.640

Question 64

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. Suppose that 500 couples each have a baby; find the mean and
standard deviation for the number of girls in the 500 babies.

Question 65

According to government data, the probability that a woman between the ages of 25 and 29 was never married is 40%. In a random survey of 10 women in this age group, what is the mean and standard deviation of the
Number that never married?

A)mean: 4; standard deviation: 1.55
B)mean: 6; standard deviation: 1.55
C)mean: 6; standard deviation: 155
D)mean: 4; standard deviation: 2.4

Question 66

According to government data, the probability that a woman between the ages of 25 and 29 was never married is 40%. In a random survey of 10 women in this age group, what is the probability that two or fewer were never
Married?

A)0.167
B)1.002
C)0.013
D)0.161

Question 67

The probability that a tennis set will go to a tiebreaker is 16%. In 220 randomly selected tennis sets, what is the mean and the standard deviation of the number of tiebreakers?

A)mean: 35.2; standard deviation: 5.44
B)mean: 35.2; standard deviation: 5.93
C)mean: 33; standard deviation: 5.44
D)mean: 33; standard deviation: 5.93

Question 68

The probability that a tennis set will go to a tie-breaker is 14%. What is the probability that two of three sets will go to tie-breakers?

A)0.051
B)0.14
C)0.311
D)0.0196

Question 69

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 boys in ten births.

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

Question 70

According to police sources, a car with a certain protection system will be recovered 90% of the time. If 600 stolen cars are randomly selected, what is the mean and standard deviation of the number of cars recovered
After being stolen?

A)mean: 540; standard deviation: 7.35
B)mean: 540; standard deviation: 54
C)mean: 306: standard deviation: 7.35
D)mean: 306: standard deviation: 54

Question 71

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 boys in ten births.

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

Question 72

According to police sources, a car with a certain protection system will be recovered 89% of the time. Find the probability that 3 of 7 stolen cars will be recovered.

A)0.004
B)0.429
C)0.89
D)0.11

Question 73

Fifty percent of the people that get mail-order catalogs order something. Find the probability that exactly two of 10 people getting these catalogs will order something.

A)0.044
B)0.200
C)0.001
D)11.250

Question 74

The probability that a house in an urban area will be burglarized is 5%. If 82 houses are randomly selected, what is the probability that none of the houses will be burglarized?

A)0.015
B)0.050
C)0.000
D)0.001

Question 75

A test consists of 10 true or false questions. To pass the test 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 test?

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

Question 76

A recent survey found that 63% of all adults over 50 wear glasses for driving. In a random sample of 100 adults over 50, what is the mean and standard deviation of those that wear glasses?

A)mean: 63; standard deviation: 4.83
B)mean: 63; standard deviation: 7.94
C)mean: 37; standard deviation: 4.83
D)mean: 37; standard deviation: 7.94

Question 77

A test consists of 100 multiple choice questions, each with five possible answers, only one of which is correct. Find the mean and the standard deviation of the number of correct answers.

A)mean: 20; standard deviation: 4
B)mean: 20; standard deviation: 4.47
C)mean: 50; standard deviation: 4
D)mean: 50; standard deviation: 7.07

Question 78

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

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

Question 79

The probability that an individual is left-handed is 0.16. In a class of 10 students, what is the mean and standard deviation of the number of left-handers in the class?

A)mean: 1.6; standard deviation: 1.16
B)mean: 10; standard deviation: 1.16
C)mean: 1.6; standard deviation: 1.26
D)mean: 10; standard deviation: 1.26

Question 80

According to government data, the probability that a woman between the ages of 25 and 29 was never married is 40%. In a random survey of 10 women in this age group, what is the probability that at least eight were
Married?

A)0.167
B)1.002
C)0.013
D)0.161