Question 1

There are two types of random variables: discrete and continuous.

Accepted Answer

A) True 
 B)False

Question 2

Combinations are distinguishable ordered arrangements of items all of which have been drawn from a given group of items.

Accepted Answer

A) True 
 B)False

Question 3

The probability distribution of the number of accidents in Grand Rapids, Michigan, each day is given by   Based on this distribution, the expected number of accidents in a given day is:

Accepted Answer

A)  4.62 
B)  1.47 
C)  2.15 
D)  1.81 
E)  1 
A)  4.62 
B)  1.47 
C)  2.15 
D)  1.81 
E)  1

Question 4

If P(A) = 0.30, P(B) = 0.40 and P(A   B) = 0.20, then P(A / B) is:

Accepted Answer

A)  0.12 
B)  0.08 
C)  0.67 
D)  0.50 
E)  0.3 
A)  0.12 
B)  0.08 
C)  0.67 
D)  0.50 
E)  0.3

Question 5

Bayes' Rule is a formula for revising an initial subjective (prior) probability value on the basis of results obtained by an empirical investigation and for, thus, obtaining a new (posterior) probability value.

Accepted Answer

A) True 
 B)False

Question 6

The probability distribution for a discrete variable x is a formula, a table, or a graph providing p(x), the probability associated with each of the values of x.

Accepted Answer

A) True 
 B)False

Question 7

The sample space for an experiment can be represented by:

Accepted Answer

A)  a joint probability table 
B)  the additive rule of probability 
C)  the multiplicative rule of probability 
D)  a tree diagram 
E)  None of these 
A)  a joint probability table 
B)  the additive rule of probability 
C)  the multiplicative rule of probability 
D)  a tree diagram 
E)  None of these

Question 8

The weight of a box of candy bars is an example of a discrete random variable since there are only a specific number of bars in the box.

Accepted Answer

A) True 
 B)False

Question 9

Which of following statements is true regarding the probability distribution for a discrete random variable X?

Accepted Answer

A)  The probabilities must be nonnegative. 
B)  The probabilities must sum to 1. 
C)  The random variable must take on positive values between 0 and 1. 
D)  Both the probabilities must be nonnegative and the probabilities must sum to 1. 
E)  Both the probabilities must be nonnegative and the random variable must take on positive values between 0 and 1. 
A)  The probabilities must be nonnegative. 
B)  The probabilities must sum to 1. 
C)  The random variable must take on positive values between 0 and 1. 
D)  Both the probabilities must be nonnegative and the probabilities must sum to 1. 
E)  Both the probabilities must be nonnegative and the random variable must take on positive values between 0 and 1.

Question 10

All the outcomes contained in one or the other of two events (or possibly in both) constitute the union of two events.

Accepted Answer

A) True 
 B)False

Question 11

If P(A) = 0.60, P(B) = 0.40, and P(B / A) = 0.60, then P(A / B) = 0.24.

Accepted Answer

A) True 
 B)False

Question 12

A federal agency is trying to decide which of two waste management projects to investigate as the source of air pollution. In the past, projects of the first type were in violation of air quality standards with probability 0.3 on any given day, while projects of the second type were in violation of air quality standards with probability 0.25 on any given day. It is not possible for both projects to pollute the air in one day. Let Ai, i = 1, 2, denote that project of type i was in violation of air quality standards.
a. Find the probability of an air pollution problem caused by either the first project or the second project.
______________
b. If the first project is violating air quality standards, what is the probability the second project is also violating federal air quality standards?
______________

Accepted Answer

Question 13

A table, graph, or formula that associates each possible value of a discrete random variable, x with its probability of occurrence, p(x), is called a discrete probability distribution.

Accepted Answer

A) True 
 B)False

Question 14

If P(A) = 0.3, P(A   B) = 0.7, and P(A   B) = 0.2, then P(B) = 0.2.

Accepted Answer

A) True 
 B)False

Question 15

An election is being held to fill two "at large" city council seats. Two Republicans and three Democrats are running for office. Assume the candidates are equally likely to be elected, and independent of each other.
a. What are the possible outcomes of the election?
______________
b. What is the probability both seats are filled by Republicans?
______________
c. What is the probability one Republican and one Democrat are elected to the two city council seats?
______________

Accepted Answer

a. RR, RD,

Question 16

When a patient who is complaining of several specific symptoms arrives at a doctor's office, the doctor who makes the diagnosis says that she is 90% certain that the patient has the flu, it is likely that she is basing her assessment on relative frequency approach of assigning probabilities.

Accepted Answer

A) True 
 B)False

Question 17

A tree diagram is a listing of all simple events of an experiment.

Accepted Answer

A) True 
 B)False

Question 18

Let the random variable x represent the number of cars owned by a family. Assume that x can take on five values: 0, 1, 2, 3, 4. A partial probability distribution is shown below:
   
a. Find the probability that a family owns three cars.
______________
b. Find the probability that a family owns between 1 and 3 cars, inclusive.
______________
c. Find the probability that a family owns no more than one car.
______________
d. What is the probability that a family owns more than two cars?
______________
e. What is the probability that a family owns at most 3 cars?
______________

Accepted Answer

a. 0.3; b.

Question 19

Which of the following clearly describes the general multiplicative rule of probability?

Accepted Answer

A)  It is a rule of probability theory that is used to compute the probability for the occurrence of a union of two or more events: for any two events, A and B,. 
B)  It is a rule of probability theory that is used to compute the probability for the occurrence of a union of two or more events: for any two events A and B,. 
C)  It is a rule of probability theory that is used to compute the probability for an intersection of two or more events: for any two events, A and B, 
D)  It is a rule of probability theory that is used to compute the probability for an intersection of two or more events: for any two events A and B, 
E)  All of these. 
A)  It is a rule of probability theory that is used to compute the probability for the occurrence of a union of two or more events: for any two events, A and B,. 
B)  It is a rule of probability theory that is used to compute the probability for the occurrence of a union of two or more events: for any two events A and B,. 
C)  It is a rule of probability theory that is used to compute the probability for an intersection of two or more events: for any two events, A and B, 
D)  It is a rule of probability theory that is used to compute the probability for an intersection of two or more events: for any two events A and B, 
E)  All of these.

Question 20

From experience, a shipping company knows that the cost of delivering a small package within 24 hours is $16.20. The company charges $16.95 for shipment but guarantees to refund the charge if delivery is not made within 24 hours. If the company fails to deliver only 3% of its packages within the 24-hour period, what is the expected gain per package?
______________

Accepted Answer

The answer of From experience, a shipping company knows that...

There are two types of random variables: discrete and continuous.

Combinations are distinguishable ordered arrangements of items all of which have been drawn from a given group of items.

The probability distribution of the number of accidents in Grand Rapids, Michigan, each day is given by Based on this distribution, the expected number of accidents in a given day is:

If P(A) = 0.30, P(B) = 0.40 and P(A B) = 0.20, then P(A / B) is:

Bayes' Rule is a formula for revising an initial subjective (prior) probability value on the basis of results obtained by an empirical investigation and for, thus, obtaining a new (posterior) probability value.

The probability distribution for a discrete variable x is a formula, a table, or a graph providing p(x), the probability associated with each of the values of x.

The sample space for an experiment can be represented by:

The weight of a box of candy bars is an example of a discrete random variable since there are only a specific number of bars in the box.

Which of following statements is true regarding the probability distribution for a discrete random variable X?

All the outcomes contained in one or the other of two events (or possibly in both) constitute the union of two events.

If P(A) = 0.60, P(B) = 0.40, and P(B / A) = 0.60, then P(A / B) = 0.24.

A table, graph, or formula that associates each possible value of a discrete random variable, x with its probability of occurrence, p(x), is called a discrete probability distribution.

If P(A) = 0.3, P(A B) = 0.7, and P(A B) = 0.2, then P(B) = 0.2.

When a patient who is complaining of several specific symptoms arrives at a doctor's office, the doctor who makes the diagnosis says that she is 90% certain that the patient has the flu, it is likely that she is basing her assessment on relative frequency approach of assigning probabilities.

A tree diagram is a listing of all simple events of an experiment.

Which of the following clearly describes the general multiplicative rule of probability?

Describing Data With Graphs

Describing Data With Numerical Measures

Describing Bivariate Data

Several Useful Discrete Distributions

The Normal Probability Distribution

Sampling Distributions

Large-Sample Estimation

Large-Sample Tests of Hypotheses

Inference From Small Samples

The Analysis of Variance

Linear Regression and Correlation

Multiple Regression Analysis

Analysis of Categorical Data

Nonparametric Statistics

Filters

Exam 4: Probability and Probability Distributions

There are two types of random variables: discrete and continuous.

Combinations are distinguishable ordered arrangements of items all of which have been drawn from a given group of items.

The probability distribution of the number of accidents in Grand Rapids, Michigan, each day is given by Based on this distribution, the expected number of accidents in a given day is:

If P(A) = 0.30, P(B) = 0.40 and P(A B) = 0.20, then P(A / B) is:

Bayes' Rule is a formula for revising an initial subjective (prior) probability value on the basis of results obtained by an empirical investigation and for, thus, obtaining a new (posterior) probability value.

The probability distribution for a discrete variable x is a formula, a table, or a graph providing p(x), the probability associated with each of the values of x.

The sample space for an experiment can be represented by:

The weight of a box of candy bars is an example of a discrete random variable since there are only a specific number of bars in the box.

Which of following statements is true regarding the probability distribution for a discrete random variable X?

All the outcomes contained in one or the other of two events (or possibly in both) constitute the union of two events.

If P(A) = 0.60, P(B) = 0.40, and P(B / A) = 0.60, then P(A / B) = 0.24.

A table, graph, or formula that associates each possible value of a discrete random variable, x with its probability of occurrence, p(x), is called a discrete probability distribution.

If P(A) = 0.3, P(A B) = 0.7, and P(A B) = 0.2, then P(B) = 0.2.

When a patient who is complaining of several specific symptoms arrives at a doctor's office, the doctor who makes the diagnosis says that she is 90% certain that the patient has the flu, it is likely that she is basing her assessment on relative frequency approach of assigning probabilities.

A tree diagram is a listing of all simple events of an experiment.

Which of the following clearly describes the general multiplicative rule of probability?

Describing Data With Graphs

Describing Data With Numerical Measures

Describing Bivariate Data

Several Useful Discrete Distributions

The Normal Probability Distribution

Sampling Distributions

Large-Sample Estimation

Large-Sample Tests of Hypotheses

Inference From Small Samples

The Analysis of Variance

Linear Regression and Correlation

Multiple Regression Analysis

Analysis of Categorical Data

Nonparametric Statistics

Filters