Question 1

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

Accepted Answer

A) ​2.887 
B) ​3.464 
C) 8.333 
D) ​12 
A) ​2.887 
B) ​3.464 
C) 8.333 
D) ​12 A

Question 2

A health conscious student faithfully wears a device that tracks his steps. Suppose that the distribution of the number of steps he takes is normally distributed with a mean of 10,000 and a standard deviation of 1,500 steps. How many steps would he have to take to make the cut for the top 5% for his distribution? ​​

Accepted Answer

A) 7,533 
B) 8,078 
C) 10,000 
D) 12,467 
A) 7,533 
B) 8,078 
C) 10,000 
D) 12,467 D

Question 3

Which of the following is a discrete random variable?

Accepted Answer

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. 
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. A

Question 4

A bucket contains 2 red balls, 4 yellow balls, and 5 purple balls. One ball is taken from the bucket and then replaced. Another ball is taken from the bucket. Are the events of pulling first ball is red then a purple one independent or dependent?

Accepted Answer

The answer of A bucket contains 2 red balls, 4...

Question 5

The cross tabulation below classifies employees of a communications company by age and field of expertise. Use the given information to create a joint probability table.
​ $$\begin{array} { | l | c | c | c | c | } 
\hline & \text { Under } \mathbf { 3 5 } & \mathbf { 3 5 } - \mathbf { 4 4 } & \mathbf { 4 5 } + & \text { Total } \
\hline \text { Engineering } & 8,399 & 8,663 & 7,072 & \mathbf { 2 4 , 1 3 4 } \
\hline \text { Business } & 14,515 & 14,988 & 26,683 & \mathbf { 5 6 , 1 8 6 } \
\hline \text { Education } & 6,738 & 5,657 & 8,669 & \mathbf { 2 1 , 0 6 4 } \
\hline \text { Liberal Arts } & 11,415 & 11,484 & 12,111 & \mathbf { 3 5 , 0 1 0 } \
\hline  { \text { Total } } & \mathbf { 4 1 , 0 6 7 } & \mathbf { 4 0 , 7 9 2 } & \mathbf { 5 4 , 5 3 5 } & \mathbf { 1 3 6 , 3 9 4 } \
\hline
\end{array}$$ ​

Accepted Answer

The answer of The cross tabulation below classifies employees of...

Question 6

Consider a random experiment of rolling 2 dice. The sample space for rolling two dice is shown. Let S be the set of all ordered pairs listed in the figure. What is probability of rolling a 7?

Accepted Answer

0.1667 or

Question 7

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

Accepted Answer

A) joint events. 
B) the complement of the event. 
C) simple events. 
D) independent events. 
A) joint events. 
B) the complement of the event. 
C) simple events. 
D) independent events.

Question 8

The time in seconds that it takes a production worker to inspect an item has an exponential distribution with mean 15 seconds. What proportion of inspection times is less than 10 seconds?
​
​

Accepted Answer

The answer of The time in seconds that it takes...

Question 9

All of the following are examples of discrete random variables except ​​

Accepted Answer

A) number of tickets sold. 
B) marital status. 
C) time. 
D) population of a city. 
A) number of tickets sold. 
B) marital status. 
C) time. 
D) population of a city.

Question 10

For the standard normal probability distribution, what percent of the curve lies to the left of the mean?
​

Accepted Answer

The answer of For the standard normal probability distribution, what...

Question 11

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

Accepted Answer

A) ​posterior 
B) ​conditional 
C) empirical 
D) ​prior 
A) ​posterior 
B) ​conditional 
C) empirical 
D) ​prior

Question 12

A(n) ________________ is a description of how probabilities are distributed over the values of a random variable.​

Accepted Answer

A) ​probability distribution 
B) ​mass function of an event 
C) ​density function 
D) ​expected value 
A) ​probability distribution 
B) ​mass function of an event 
C) ​density function 
D) ​expected value

Question 13

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

Accepted Answer

A) union 
B) Venn diagram 
C) intersection 
D) subset 
A) union 
B) Venn diagram 
C) intersection 
D) subset

Question 14

The triangular distribution is a good model for____________ distributions. ​​

Accepted Answer

A) uniform 
B) skewed 
C) normal 
A) uniform 
B) skewed 
C) normal

Question 15

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

Accepted Answer

A) categorical variable. 
B) discrete random variable. 
C) continuous random variable. 
A) categorical variable. 
B) discrete random variable. 
C) continuous random variable.

Question 16

In a normal​ distribution, which is​ greater, the mean or the​ median? ​​

Accepted Answer

A) Mean 
B) Median 
C) Neither (they are equal) 
D) Cannot be determined with the information provided 
A) Mean 
B) Median 
C) Neither (they are equal) 
D) Cannot be determined with the information provided

Question 17

In the probability table below, which value is a marginal probability? ?? $$\begin{array} { | l | l | l | c | } 
\hline &  { \text { Completed } } \
\hline \text { Obstacle Course Level } & \text { No } & \text { Yes } & \text { Total } \
\hline \text { Challenging } & 0.4 & 0.3 & 0.7 \
\hline \text { Easy } & 0.1 & 0.2 & 0.3 \
\hline \text { Total } & 0.5 & 0.5 & 1 \
\hline
\end{array}$$

Accepted Answer

A) 0.1 
B) 1 
C) 0.5 
D) 0.4 
A) 0.1 
B) 1 
C) 0.5 
D) 0.4

Question 18

A nickel and a dime are tossed. If an event is defined as a single toss of both coins where at least one head appears, what is the complement of that event?

Accepted Answer

The answer of A nickel and a dime are tossed....

Question 19

Could this curve represent a normal distribution?
​

Accepted Answer

The answer of Could this curve represent a normal distribution?
​...

Question 20

What is the total area under the normal distribution curve? ​​

Accepted Answer

A) It depends upon the mean and standard deviation 
B) It must be calculated 
C) 1 
D) 100 
A) It depends upon the mean and standard deviation 
B) It must be calculated 
C) 1 
D) 100

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

Which of the following is a discrete random variable?

A bucket contains 2 red balls, 4 yellow balls, and 5 purple balls. One ball is taken from the bucket and then replaced. Another ball is taken from the bucket. Are the events of pulling first ball is red then a purple one independent or dependent?

Consider a random experiment of rolling 2 dice. The sample space for rolling two dice is shown. Let S be the set of all ordered pairs listed in the figure. What is probability of rolling a 7?

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

The time in seconds that it takes a production worker to inspect an item has an exponential distribution with mean 15 seconds. What proportion of inspection times is less than 10 seconds?

All of the following are examples of discrete random variables except

For the standard normal probability distribution, what percent of the curve lies to the left of the mean?

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

A(n) ________________ is a description of how probabilities are distributed over the values of a random variable.

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

The triangular distribution is a good model for____________ distributions.

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

In a normal distribution, which is greater, the mean or the median?

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

A nickel and a dime are tossed. If an event is defined as a single toss of both coins where at least one head appears, what is the complement of that event?

Could this curve represent a normal distribution?

What is the total area under the normal distribution curve?

Introduction

Descriptive Statistics

Data Visualization

Descriptive Data Mining

Statistical Inference

Linear Regression

Time Series Analysis and Forecasting

Predictive Data Mining

Spreadsheet Models

Linear Optimization Models

Integer Linear Optimization Models

Nonlinear Optimization Models

Monte Carlo Simulation

Decision Analysis

Filters

Exam 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.

Which of the following is a discrete random variable?

A bucket contains 2 red balls, 4 yellow balls, and 5 purple balls. One ball is taken from the bucket and then replaced. Another ball is taken from the bucket. Are the events of pulling first ball is red then a purple one independent or dependent?

Consider a random experiment of rolling 2 dice. The sample space for rolling two dice is shown. Let S be the set of all ordered pairs listed in the figure. What is probability of rolling a 7?

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

The time in seconds that it takes a production worker to inspect an item has an exponential distribution with mean 15 seconds. What proportion of inspection times is less than 10 seconds? ​ ​

All of the following are examples of discrete random variables except ​​

For the standard normal probability distribution, what percent of the curve lies to the left of the mean? ​

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

A(n) ________________ is a description of how probabilities are distributed over the values of a random variable.​

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

The triangular distribution is a good model for____________ distributions. ​​

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

In a normal​ distribution, which is​ greater, the mean or the​ median? ​​

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

A nickel and a dime are tossed. If an event is defined as a single toss of both coins where at least one head appears, what is the complement of that event?

Could this curve represent a normal distribution? ​

What is the total area under the normal distribution curve? ​​

Introduction

Descriptive Statistics

Data Visualization

Descriptive Data Mining

Statistical Inference

Linear Regression

Time Series Analysis and Forecasting

Predictive Data Mining

Spreadsheet Models

Linear Optimization Models

Integer Linear Optimization Models

Nonlinear Optimization Models

Monte Carlo Simulation

Decision Analysis

Filters

The time in seconds that it takes a production worker to inspect an item has an exponential distribution with mean 15 seconds. What proportion of inspection times is less than 10 seconds?

All of the following are examples of discrete random variables except

For the standard normal probability distribution, what percent of the curve lies to the left of the mean?

A(n) ________________ is a description of how probabilities are distributed over the values of a random variable.

The triangular distribution is a good model for____________ distributions.

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

In a normal distribution, which is greater, the mean or the median?

Could this curve represent a normal distribution?

What is the total area under the normal distribution curve?