Question 1

The random variable X is known to be uniformly distributed between 2 and 12. Compute the standard deviation of X.
A)2.887
B)3.464
C)8.333
D)12

Accepted Answer

The standard deviation of a uniform distribution is given by the formula:σ = (b - a) / √12where a and b are the lower and upper bounds of the distribution, respectively.In this case, a = 2 and b = 12, so:σ = (12 - 2) / √12 = 10 / √12 = 2.887Therefore, the standard deviation of X is 2.887.

Question 2

A __________ describes the range and relative likelihood of all possible values for a random variable.
A)probability distribution for a random variable
B)probability mass function of an event
C)density function
D)probability

Accepted Answer

A probability distribution for a random variable will list all possible values of the variable and the corresponding probabilities or likelihoods of each value occurring. This fully describes the range and relative likelihood of all possible values. Probability mass functions and density functions are specific types of probability distributions. Probability, while related, is not a complete description of the range and likelihood of all possible values.

Question 3

The __________ probability distribution can be used to estimate the number of vehicles that go through an intersection during the lunch hour.
A)binomial
B)normal
C)triangular
D)Poisson

Accepted Answer

The Poisson probability distribution is appropriate for estimating the number of occurrences of a specific event over a period of time or within a certain area. In this case, the number of vehicles passing through an intersection can be seen as a count of events within a certain time period, making the Poisson distribution an appropriate choice. The binomial distribution is used for counting the number of successes or failures in a fixed number of trials. The normal distribution is used for continuous data with a symmetric and bell-shaped curve. The triangular distribution is used when there is uncertainty about the value of a variable, but some boundaries are known.

Question 4

A joint probability is the
A)sum of the probabilities of two events.
B)probability of the intersection of two events.
C)probability of the union of two events.
D)sum of the probabilities of two independent events.

Accepted Answer

Joint probability refers to the probability of the intersection of two events, meaning the probability of both events occurring simultaneously.

Question 5

Which of the following is a discrete random variable?
A)The number of times a student guesses the answers to questions on a certain test
B)The amount of gasoline purchased by a customer
C)The amount of mercury found in fish caught in the Gulf of Mexico
D)The height of water-oak trees

Accepted Answer

A discrete random variable is one that can only take a finite or countably infinite set of values. In this case, the number of times a student guesses answers on a test can only take on specific whole numbers, making it a discrete random variable. The other options (gasoline purchased, amount of mercury, height of trees) can take on any range of continuous values and are therefore not discrete random variables.

Question 6

If a z-score is zero, then the corresponding x-value must be equal to the
A)mean.
B)median.
C)mode.
D)standard deviation.

Accepted Answer

A z-score of zero indicates that the x-value is equal to the mean of the distribution.

Question 7

An initial estimate of the probabilities of events is a __________ probability.
A)posterior
B)conditional
C)empirical
D)prior

Accepted Answer

Prior probability is an initial estimate or assumption about the probability of an event occurring, based on prior knowledge or experience.

Question 8

A variable that can only take on specific numeric values is called a
A)categorical variable.
B)discrete random variable.
C)continuous random variable.

Accepted Answer

A categorical variable can take on non-numeric values, while a discrete random variable can only take on specific numeric values. A continuous random variable can take on any value within a range, including non-numeric values. Therefore, the best choice is B.

Question 9

The random variable X is known to be uniformly distributed between 2 and 12. Compute E(X), the expected value of the distribution.
A)4
B)5
C)6
D)7

Accepted Answer

The expected value E(X) of a uniformly distributed random variable between a and b is given by (a + b) / 2. Here, a = 2 and b = 12, so E(X) = (2 + 12) / 2 = 7.

Question 10

All the events in the sample space that are not part of the specified event are called
A)joint events.
B)the complement of the event.
C)simple events.
D)independent events.

Accepted Answer

The complement of an event includes all outcomes in the sample space that are not part of the specified event.

Question 11

Two events are independent if
A)the two events occur at the same time.
B)the probability of one or both events is greater than 1.
C)P(A | B) = P(A) or P(B | A) = P(B).
D)None of these are correct.

Accepted Answer

Two events are independent if the occurrence of one event does not affect the probability of the other event. In other words, P(A | B) = P(A) or P(B | A) = P(B). Therefore, option C is the correct answer. The other options are incorrect. Option A implies simultaneous occurrence, which is not a defining factor for independence. Option B implies an impossible scenario since the probability of an event cannot be greater than 1. Option D is a blanket statement that does not provide any information.

Question 12

An experiment consists of determining the speed of automobiles on a highway by the use of radar equipment. The random variable in this experiment is a
A)discrete random variable.
B)continuous random variable.
C)complex random variable.
D)categorical random variable.

Accepted Answer

The speed of automobiles on a highway can take on any value within a range (e.g. 0-100 mph), making it a continuous random variable.

Question 13

Which statement is true about mutually exclusive events?
A)If events A and B cannot occur at the same time, they are called mutually exclusive.
B)If either event A or event B must occur, they are called mutually exclusive.
C)P(A) + P(B) = 1 for any events A and B that are mutually exclusive.
D)None of these are correct.

Accepted Answer

Mutually exclusive events cannot occur at the same time, meaning if one event happens, then the other cannot happen. This is the definition of mutually exclusive events.

Question 14

Bayes' theorem is a method used to compute __________ probabilities.
A)posterior
B)conditional
C)empirical
D)prior

Accepted Answer

Bayes' theorem is used to compute posterior probabilities, which are updated probabilities of a hypothesis given new evidence.

Question 15

All of the following are examples of discrete random variables except
A)number of tickets sold.
B)marital status.
C)time.
D)population of a city.

Accepted Answer

Time is a continuous random variable because it can take on any value within an interval and is not countable.

Question 16

In the probability table below, which value is a marginal probability? ​
Completed
Obstacle Course Level
No
Yes
Total
Challenging
0)4
0)3
0)7
Easy
0)1
0)2
0)3
Total
0)5
0)5
1)0
A)0.1
B)1.0
C)0.5
D)0.4

Accepted Answer

Marginal probability refers to the probability of a single event occurring, without consideration of any other events. In the table, 0.5 (or 5 out of 10) represents the marginal probability of completing the obstacle course (Yes) or not completing it (No), as it is the total probability of each outcome divided by the total number of attempts.

Question 17

Probability is the
A)number of successes divided by the number of failures.
B)numerical measure of the likelihood that an event will occur.
C)chance that an event will not happen.
D)number of successes divided by the standard deviation of the distribution.

Accepted Answer

Probability is a numerical measure of the likelihood that an event will occur. It is expressed as a number between 0 and 1, with 0 indicating that the event is impossible and 1 indicating that the event is certain.

Question 18

Sample space is
A)a process that results in some outcome.
B)the collection of all possible outcomes.
C)the collection of events
D)a subgroup of a population/the likelihood of an outcome.

Accepted Answer

The sample space is the collection of all possible outcomes that can occur in an experiment, so it includes every outcome that could happen. It is not the process itself (A), nor is it a collection of events (C). It is also not a subgroup of a population (D) or the likelihood of an outcome.

Question 19

The event containing the outcomes belonging to A or B or both is the __________ of A and B.
A)union
B)Venn diagram
C)intersection
D)complement

Accepted Answer

The union of events A and B includes all the outcomes that belong to either A or B or both.

Question 20

Which of the following statements is correct?
A)The binomial and normal distributions are both discrete probability distributions.
B)The binomial and normal distributions are both continuous probability distributions.
C)The binomial distribution is a continuous probability distribution, and the normal distribution is a discrete probability distribution.
D)The binomial distribution is a discrete probability distribution and the normal distribution is a continuous probability distribution.

Accepted Answer

The binomial distribution is a discrete probability distribution that models the probability of a certain number of successes in a fixed number of trials, while the normal distribution is a continuous probability distribution that models the distribution of a random variable that is normally distributed.

Quiz 5: Probability: an Introduction to Modeling Uncertainty

The random variable X is known to be uniformly distributed between 2 and 12. Compute the standard deviation of X.

A __________ describes the range and relative likelihood of all possible values for a random variable.

The __________ probability distribution can be used to estimate the number of vehicles that go through an intersection during the lunch hour.

A joint probability is the

Which of the following is a discrete random variable?

If a z-score is zero, then the corresponding x-value must be equal to the

An initial estimate of the probabilities of events is a __________ probability.

A variable that can only take on specific numeric values is called a

The random variable X is known to be uniformly distributed between 2 and 12. Compute E(X) , the expected value of the distribution.

All the events in the sample space that are not part of the specified event are called

Two events are independent if

An experiment consists of determining the speed of automobiles on a highway by the use of radar equipment. The random variable in this experiment is a

Which statement is true about mutually exclusive events?

Bayes' theorem is a method used to compute __________ probabilities.

All of the following are examples of discrete random variables except

In the probability table below, which value is a marginal probability? Completed Obstacle Course Level No Yes Total Challenging 0) 4 0) 3 0) 7 Easy 0) 1 0) 2 0) 3 Total 0) 5 0) 5 1) 0

Probability is the

Sample space is

The event containing the outcomes belonging to A or B or both is the __________ of A and B.

Which of the following statements is correct?