Deck 4: Discrete Random Variables

Question 1

Classify the following random variable according to whether it is discrete or continuous. The blood pressures of a group of students the day before the final exam

A)continuous
B)discrete

Answer 1

A

Question 2

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

A)discrete
B)continuous

Answer 2

A

Question 3

Management at a home improvement store randomly selected 120 customers and observed their shopping habits. They recorded the number of items 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
Managers of the home improvement store.

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

Answer 3

B

Question 4

Classify the following random variable according to whether it is discrete or continuous. The speed of a car on a Los Angeles freeway during rush hour traffic

A)discrete
B)continuous

Question 5

Classify the following random variable according to whether it is discrete or continuous. The number of pills in a container of vitamins

A)discrete
B)continuous

Question 6

Explain why the following is or is not a valid probability distribution for the discrete
random variable x.

Question 7

Classify the following random variable according to whether it is discrete or continuous. The height of a player on a basketball team

A)continuous
B)discrete

Question 8

Consider the given discrete probability distribution. Construct a graph for p(x).

Question 9

A coin is flipped 6 times. The variable x represents the number of tails obtained.
List the possible values of x. Is x discrete or continuous? Explain.

Question 10

A bottle contains 16 ounces of water. The variable x represents the volume, in ounces, of
water remaining in the bottle after the first drink is taken. What are the natural bounds for
the values of x? Is x discrete or continuous? Explain.

Question 11

Explain why the following is or is not a valid probability distribution for the discrete
random variable x.

Question 12

The Fresh Oven Bakery knows that the number of pies it can sell varies from day to day. The owner believes that on 50% of the days she sells 100 pies. On another 25% of the days she sells 150
Pies, and she sells 200 pies on the remaining 25% of the days. To make sure she has enough
Product, the owner bakes 200 pies each day at a cost of $1.50 each. Assume any pies that go unsold
Are thrown out at the end of the day. If she sells the pies for $3 each, find the probability
Distribution for her daily profit.

Question 13

Explain why the following is or is not a valid probability distribution for the discrete
random variable x.

Question 14

A discrete random variable x can assume five possible values: 2, 3, 5, 8, 10. Its probability distribution is shown below. Find the probability for the value of x = 5.

A)0.7
B)0.1
C)0.2
D)0.3

Question 15

Classify the following random variable according to whether it is discrete or continuous. The number of phone calls to the attendance office of a high school on any given school day

A)continuous
B)discrete

Question 16

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

A)continuous
B)discrete

Question 17

The school newspaper surveyed 100 commuter students and asked two questions. First, students were asked how many courses they were currently enrolled in. Second, the commuter students
Were asked to estimate how long it took them to drive to campus. Considering these two variables,
Number of courses would best be considered a _________ variable and drive time would be
Considered a _________ variable.

A)discrete; continuous
B)continuous; discrete
C)discrete; discrete
D)continuous; continuous

Question 18

Explain why the following is or is not a valid probability distribution for the discrete
random variable x.

Question 19

50 students were randomly sampled and asked questions about their exercise habits. One of the questions they were asked concerned the frequency of exercise, defined to be the number of times
They exercised in a week. This variable would be characterized as which type of random variable?

A)continuous
B)discrete

Question 20

Classify the following random variable according to whether it is discrete or continuous. The temperature in degrees Fahrenheit on July 4th in Juneau, Alaska

A)discrete
B)continuous

Question 21

Consider the given discrete probability distribution. Find the probability that x exceeds 4.

Question 22

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

A)mean: 1.50; standard deviation: .76
B)mean: 2.25; standard deviation: .76
C)mean: 2.25; standard deviation: .87
D)mean: 1.50; standard deviation: .87

Question 23

A discrete random variable x can assume five possible values: 2, 3, 5, 8, 10. Its probability distribution is shown below. Find the probability that the random variable x is a value greater
Than 5.

A)0.60
B)0.70
C)0.40
D)0.30

Question 24

An airline has requests for standby flights at half of the usual one-way air fare. Past
experience has shown that these passengers have about a 1 in 5 chance of getting on the
standby flight. When they fail to get on a flight as a standby, the 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
$150 and the cost of flying first class is $315. 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 25

Question 26

A discrete random variable x can assume five possible values: 2, 3, 5, 8, 10. Its probability distribution is shown below. Find the mean of the distribution.

Question 27

Question 28

Mamma Temte bakes six pies each day at a cost of $2 each. On 31% of the days she sells only two pies. On 18% of the days, she sells 4 pies, and on the remaining 51% of the days, she sells all six
Pies. If Mama Temte sells her pies for $4 each, what is her expected profit for a dayʹs worth of pies?
[Assume that any leftover pies are given away.]

A)$5.60
B)-$8.00
C)$17.60
D)-$7.60

Question 29

The expected value of a discrete random variable must be one of the values in which the random
variable can result.

Question 30

A lab orders a shipment of 100 frogs each week. Prices for the weekly shipments of frogs follow the distribution below: How much should the lab budget for next yearʹs frog orders assuming this distribution does not
Change? (Hint: Find the expected price and assume 52 weeks per year.)

A)$1275.00
B)$663.00
C)$12.75
D)$3,447,600.00

Question 31

A discrete random variable x can assume five possible values: 2, 3, 5, 8, 10. Its probability distribution is shown below. Find the standard deviation of the distribution.

Question 32

Question 33

An automobile insurance company estimates the following loss probabilities for the next
year on a $25,000 sports 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 $610 profit per policy sold?

Question 34

Calculate the mean for the discrete probability distribution shown here.

Question 35

A lab orders a shipment of 100 frogs each week. Prices for the weekly shipments of frogs follow the distribution below:

Question 36

Consider the given discrete probability distribution. Find the probability that x equals 5.

Question 37

Consider the given discrete probability distribution. Construct a graph for p(x).

Question 38

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

A)10
B)11.41
C)11.2
D)20

Question 39

Question 40

A dice game involves rolling three dice and betting on one of the six numbers that are on the dice. The game costs $12 to play, and you win if the number you bet appears on any of the dice. The
Distribution for the outcomes of the game (including the profit)is shown below:

Question 41

A recent article in the paper claims that business ethics are at an all-time low. Reporting on a recent sample, the paper claims that 45% of all employees believe their company president
Possesses low ethical standards. Suppose 20 of a companyʹs employees are randomly and
Independently sampled and asked if they believe their company president has low ethical
Standards and their years of experience at the company. Could the probability distribution for the
Number of years of experience be modelled by a binomial probability distribution?

A)Yes, the sample is a random and independent sample.
B)No, a binomial distribution requires only two possible outcomes for each experimental unit sampled.
C)No, the employees would not be considered independent in the present sample.
D)Yes, the sample size is n = 20.

Question 42

Question 43

Question 44

The binomial distribution can be used to model the number of rare events that occur over a given
time period.

Question 45

Question 46

A recent study suggested that 70% of all eligible voters will vote in the next presidential election. Suppose 20 eligible voters were randomly selected from the population of all eligible voters.
Which of the following is necessary for this problem to be analyzed using the binomial random
Variable?
I. There are two outcomes possible for each of the 20 voters sampled.
II. The outcomes of the 20 voters must be considered independent of one another.
III. The probability a voter will actually vote is 0.70, the probability they wonʹt is 0.30.

A)I only
B)I, II, and III
C)II only
D)III only

Question 47

Which binomial probability is represented on the screen below?

A)The probability of 2 successes in 8 trials where the probability of success is .3.
B)The probability of 8 successes in 2 trials where the probability of success is .3.
C)The probability of 8 failures in 2 trials where the probability of failure is .3.
D)The probability of 2 successes in 8 trials where the probability of failure is .3.

Question 48

For a binomial distribution, which probability is not equal to the probability of 1 success in 5 trials where the probability of success is .4?

A)the probability of 1 success in 5 trials where the probability of failure is .6
B)the probability of 4 failures in 5 trials where the probability of success is .4
C)the probability of 4 failures in 5 trials where the probability of failure is .6
D)the probability of 4 failures in 5 trials where the probability of success is .6

Question 49

For a binomial distribution, if the probability of success is .63 on the first trial, what is the
probability of success on the second trial?

Question 50

A binomial random variable is defined to be the number of units sampled until x successes is
observed.

Question 51

Calculate the mean for the discrete probability distribution shown here.

Question 52

In a pizza takeout restaurant, the following probability distribution was obtained for the number of toppings ordered on a large pizza. Find the mean and standard deviation for the random
Variable.

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

Question 53

For a binomial distribution, if the probability of success is .48 on the first trial, what is the
probability of failure on the second trial?

Question 54

Which binomial probability is represented on the screen below?

Question 55

Solve the problem. Round to four decimal places.
If x is a binomial random variable, compute p(x)for n = 6, x = 2, p = 0.6.

A)0.1285
B)0.1451
C)0.1562
D)0.1382

Question 56

Consider the given discrete probability distribution.

Question 57

Question 58

Question 59

Find the mean and standard deviation of the probability distribution for the random
variable x, which represents the number of cars per household in a small town.

Question 60

Question 61

Solve the problem. Round to four decimal places.
A literature professor decides to give a 10-question true-false quiz. She wants to choose the passing grade such that the probability of passing a student who guesses on every question is less
Than .10. What score should be set as the lowest passing grade?

A)8
B)9
C)6
D)7

Question 62

A recent survey found that 70% of all adults over 50 wear glasses for driving. In a random sample of 70 adults over 50, what is the mean and standard deviation of the number who wear glasses?
Round to the nearest hundredth when necessary.

A)mean: 21; standard deviation: 3.83
B)mean: 49; standard deviation: 3.83
C)mean: 49; standard deviation: 7
D)mean: 21; standard deviation: 7

Question 63

Solve the problem. Round to four decimal places.
A recent article in the paper claims that business ethics are at an all-time low. Reporting on a recent sample, the paper claims that 30% of all employees believe their company president
Possesses low ethical standards. Suppose 20 of a companyʹs employees are randomly and
Independently sampled. Assuming the paperʹs claim is correct, find the probability that more than
Eight but fewer than 12 of the 20 sampled believe the companyʹs president possesses low ethical
Standards. Round to six decimal places.

A)0.226286
B)0.108193
C)0.152990
D)0.077376

Question 64

A new drug is designed to reduce a personʹs blood pressure. Thirteen randomly selected
hypertensive patients receive the new drug. Suppose the probability that a hypertensive
patientʹs blood pressure drops if he or she is untreated is 0.5. Then what is the probability
of observing 11 or more blood pressure drops in a random sample of 13 treated patients if
the new drug is in fact ineffective in reducing blood pressure? Round to six decimal
places.

Question 65

Solve the problem. Round to four decimal places.
We believe that 86% of the population of all Business Statistics students consider statistics to be an exciting subject. Suppose we randomly and independently selected 32 students from the
Population and observed fewer than five in our sample who consider statistics to be an exciting
Subject. Make an inference about the belief that 86% of the students consider statistics to be an
Exciting subject.

A)The 86% number is exactly right.
B)The 86% number is too low. The real percentage is higher than 86%.
C)The 86% number is too high. The real percentage is lower than 86%.
D)It is impossible to make any inferences about the 86% number based on this information.

Question 66

An automobile manufacturer has determined that 30% of all gas tanks that were installed
on its 2002 compact model are defective. If 9 of these cars are independently sampled,
what is the probability that more than half need new gas tanks?

Question 67

About 40% of the general population donate time and energy to community projects.
Suppose 15 people have been randomly selected from a community and each asked
whether he or she donates time and energy to community projects. Let x be the number
who donate time and energy to community projects. Use a binomial probability table to
find the probability that more than five of the 15 donate time and energy to community
projects.

Question 68

The probability that an individual is left-handed is 0.12. In a class of 10 students, what is the mean and standard deviation of the number of left-handed students? Round to the nearest hundredth
When necessary.

A)mean: 10; standard deviation: 1.1
B)mean: 1.2; standard deviation: 1.1
C)mean: 1.2; standard deviation: 1.03
D)mean: 10; standard deviation: 1.03

Question 69

Solve the problem. Round to four decimal places.
According to a recent study, 1 in every 7 women has been a victim of domestic abuse at some point in her life. Suppose we have randomly and independently sampled twenty-five women and asked
Each whether she has been a victim of domestic abuse at some point in her life. Find the probability
That at least 2 of the women sampled have been the victim of domestic abuse. Round to six decimal
Places.

A)0.713804
B)0.109532
C)0.176664
D)0.890468

Question 70

Solve the problem. Round to four decimal places.
A recent article in the paper claims that business ethics are at an all-time low. Reporting on a recent sample, the paper claims that 44% of all employees believe their company president
Possesses low ethical standards. Assume that responses were randomly and independently
Collected. A president of a local company that employs 1,000 people does not believe the paperʹs
Claim applies to her company. If the claim is true, how many of her companyʹs employees believe
That she possesses low ethical standards?

A)956
B)440
C)560
D)44

Question 71

Solve the problem. Round to four decimal places.
A recent study suggested that 70% of all eligible voters will vote in the next presidential election. Suppose 20 eligible voters were randomly selected from the population of all eligible voters. Use a
Binomial probability table to find the probability that more than 10 but fewer than 16 of the 20
Eligible voters sampled will vote in the next presidential election.

A)0.649
B)0.780
C)0.714
D)0.845

Question 72

Question 73

Question 74

Solve the problem. Round to four decimal places.
It a recent study of college students indicated that 30% of all college students had at least one tattoo. A small private college decided to randomly and independently sample 15 of their students
And ask if they have a tattoo. Use a binomial probability table to find the probability that exactly 5
Of the students reported that they did have at least one tattoo.

A)0.515
B)0.218
C)0.722
D)0.207

Question 75

Solve the problem. Round to four decimal places.
A recent study suggested that 70% of all eligible voters will vote in the next presidential election. Suppose 20 eligible voters were randomly selected from the population of all eligible voters. Use a
Binomial probability table to find the probability that more than 12 of the eligible voters sampled
Will vote in the next presidential election.

A)0.772
B)0.887
C)0.228
D)0.608
E)0.392

Question 76

Question 77

Solve the problem. Round to four decimal places.
According to a recent study, 1 in every 10 women has been a victim of domestic abuse at some point in her life. Suppose we have randomly and independently sampled twenty-five women and
Asked each whether she has been a victim of domestic abuse at some point in her life. Find the
Probability that more than 22 of the women sampled have not been the victim of domestic abuse.

A)-0.005318
B)0.265888
C)0.537094
D)0.773503

Question 78

Solve the problem. Round to four decimal places.
We believe that 95% of the population of all Business Statistics students consider statistics to be an exciting subject. Suppose we randomly and independently selected 30 students from the
Population. If the true percentage is really 95%, find the probability of observing 29 or more
Students who consider statistics to be an exciting subject. Round to six decimal places.

A)0.446458
B)0.553542
C)0.214639
D)0.338903

Question 79

Question 80

Solve the problem. Round to four decimal places.
If x is a binomial random variable, compute p(x)for n = 5, x = 3, q = 0.2.

A)0.1946
B)0.0512
C)0.0548
D)0.2048