Question 1

The sum of the probabilities of all the events in the sample space must equal 1.

Accepted Answer

A) True 
 B)False

Question 2

Discrete variables have values that can be measured.

Accepted Answer

A) True 
 B)False

Question 3

{ Find the mean of the distribution shown.

$\begin{array}{|l|c|c|c|c|}
\hline \mathrm{x} & -4 & -2 & 0 & 2 \
\hline \mathrm{P}(\mathrm{x}) & 0.17 & 0.24 & 0.50 & 0.09 \
\hline
\end{array}$

Accepted Answer

A)  -0.98 
B)  0.50 
C)  1.34 
D)  -0.02 
A)  -0.98 
B)  0.50 
C)  1.34 
D)  -0.02

Question 4

If the standard deviation of a probability distribution is 1.71, the variance is 1.31.

Accepted Answer

A) True 
 B)False

Question 5

Using the multinomial formula, find the probability of the following data.

Accepted Answer

A)  0.728 
B)  0.032 
C)  0.013 
D)  0.325 
A)  0.728 
B)  0.032 
C)  0.013 
D)  0.325

Question 6

Find the mean of the distribution shown .
$\begin{array}{|l|c|c|}
\hline \mathrm{x} & 1 & 2 \
\hline \mathrm{P}(\mathrm{x}) & 0.48 & 0.52 \
\hline
\end{array}$

Accepted Answer

A)  0.79 
B)  1.25 
C)  1.01 
D)  1.52 
A)  0.79 
B)  1.25 
C)  1.01 
D)  1.52

Question 7

Without writing down any calculations, determine the mean of the distribution shown. The variance of this probability distribution is (you can do this in your head!) $$\begin{array} { | l | c | c | c | } 
\hline \mathrm { x } & - 1 & 0 & 1 \
\hline \mathrm { P } ( \mathrm { x } ) & 0.25 & 0.50 & 0.25 \
\hline
\end{array}$$

Accepted Answer

A)  0.25 
B)  0.50 
C)  0.75 
D)  1.00 
A)  0.25 
B)  0.50 
C)  0.75 
D)  1.00

Question 8

In a binomial experiment, the outcomes of each trial must be dependent on each other.

Accepted Answer

A) True 
 B)False

Question 9

A(n) __________ probability distribution consists of the values a random variable can assume and the
corresponding probabilities of the values. 
________________________________________

Accepted Answer

The answer of A(n) __________ probability distribution consists of the...

Question 10

The supervisor at a large plant estimates that there are defective parts about 1% of the time. If the plant produces 20,000 parts in a week, what is the variance for the number of defective parts?

Accepted Answer

A)  200 
B)  198 
C)  14.1 
D)  138 
A)  200 
B)  198 
C)  14.1 
D)  138

Question 11

The probability that federal income tax returns will have 0, 1, or 2 errors is 0.53, 0.15, and 0.32, respectively. If 10 randomly selected returns are audited, what is the probability that six will have no
Errors, three will have one error, and one will have two errors?

Accepted Answer

A)  0.184 
B)  0.127 
C)  0.020 
D)  0.035 
A)  0.184 
B)  0.127 
C)  0.020 
D)  0.035

Question 12

Using the formula for the multinomial distribution, the probability of $X _ { 1 } = 2 , X _ { 2 } = 1 , X _ { 3 } = 2$ when $\mathrm { n } = 5$, $\mathrm { p } _ { 1 } = 0.4 , \mathrm { p } _ { 2 } = 0.5 , \mathrm { p } _ { 3 } = 0.1$ is

Accepted Answer

A)  $\{ 5 ! / ( 2 ! \times 1 ! \times 2 ! ) \} _ { 2 } \times 0.4 ^ { 2 } \times 0.5 ^ { 1 } \times 0.1 ^ { 2 }$ 
B)  $2 ! \times 1 ! \times 2 ! \times 0.4 ^ { 2 } \times 0.5 ^ { 1 } \times 0.1 ^ { 2 }$ 
C)  $5 ! \times 0.4 ^ { 2 } \times 0.5 ^ { 1 } \times 0.1 ^ { 2 }$ 
D)  $\{ 5 ! / ( 0.4 ! \times 0.5 ! \times 0.1 ! ) \} \times 2 ^ { 0.4 } \times 1 ^ { 0.5 } \times 2 ^ { 0.1 }$ 
A)  $\{ 5 ! / ( 2 ! \times 1 ! \times 2 ! ) \} _ { 2 } \times 0.4 ^ { 2 } \times 0.5 ^ { 1 } \times 0.1 ^ { 2 }$ 
B)  $2 ! \times 1 ! \times 2 ! \times 0.4 ^ { 2 } \times 0.5 ^ { 1 } \times 0.1 ^ { 2 }$ 
C)  $5 ! \times 0.4 ^ { 2 } \times 0.5 ^ { 1 } \times 0.1 ^ { 2 }$ 
D)  $\{ 5 ! / ( 0.4 ! \times 0.5 ! \times 0.1 ! ) \} \times 2 ^ { 0.4 } \times 1 ^ { 0.5 } \times 2 ^ { 0.1 }$

Question 13

$$\begin{array}{l}
\text { What probability value would be needed to complete the following probability distribution? }\
\begin{array} { | l | c | c | c | c | c | } 
\hline \mathrm { x } & - 5 & - 1 & 0 & 1 & 4 \
\hline \mathrm { P } ( \mathrm { x } ) & 0.09 & 0.24 & 0.16 & & 0.27 \
\hline
\end{array}
\end{array}$$

Accepted Answer

A)  0.12 
B)  0.24 
C)  0.48 
D)  There is no value that would make this a probability distribution 
A)  0.12 
B)  0.24 
C)  0.48 
D)  There is no value that would make this a probability distribution

Question 14

What of the following pairs of probability values would complete the following probability distribution? $\begin{array}{|l|c|c|c|c|c|c|}
\hline \mathrm{x} & -3 & -2 & -1 & 0 & 1 & 2 \
\hline \mathrm{P}(\mathrm{x}) & 0.09 & 0.18 & \mathrm{p}_{1} & \mathrm{p}_{2} & 0.14 & 0.23 \
\hline
\end{array}$

Accepted Answer

A)  $\mathrm { p } _ { 1 } = 0.04 , \mathrm { p } _ { 2 } = 0.59$ 
B)  $\mathrm { p } _ { 1 } = - 0.1 , \mathrm { p } _ { 2 } = 0.46$ 
C)  $\mathrm { p } _ { 1 } = 0.36 , \mathrm { p } _ { 2 } = 0.36$ 
D)  $\mathrm { p } _ { 1 } = 0 , \mathrm { p } _ { 2 } = 0.36$ 
A)  $\mathrm { p } _ { 1 } = 0.04 , \mathrm { p } _ { 2 } = 0.59$ 
B)  $\mathrm { p } _ { 1 } = - 0.1 , \mathrm { p } _ { 2 } = 0.46$ 
C)  $\mathrm { p } _ { 1 } = 0.36 , \mathrm { p } _ { 2 } = 0.36$ 
D)  $\mathrm { p } _ { 1 } = 0 , \mathrm { p } _ { 2 } = 0.36$

Question 15

One of the requirements for a binomial experiment is that there must be a __________ number of
trials. 
________________________________________

Accepted Answer

The answer of One of the requirements for a binomial...

Question 16

The figure below represents the probability distribution for selecting a number of objects out of a container. Construct a probability distribution from this graph.

Accepted Answer

\[\begin{array} { | l | r | r | r | r |

Question 17

What value would be needed to complete the following probability distribution?
$\begin{array}{|l|l|}
\hline x & P(x) \
\hline 0 & 1 / 3 \
\hline 1 & 1 / 8 \
\hline 2 & 1 / 8 \
\hline 3 & 1 / 6 \
\hline 4 & \
\hline
\end{array}$

Accepted Answer

A)  $1 / 5$ 
B)  $1 / 12$ 
C)  $1 / 4$ 
D)  $1 / 8$ 
A)  $1 / 5$ 
B)  $1 / 12$ 
C)  $1 / 4$ 
D)  $1 / 8$

Question 18

A package of 10 batteries is checked to determine if there are any dead batteries. Four batteries are checked. If one or more are dead, the package is not sold. What is the probability that the package will
Not be sold if there are actually three dead batteries in the package?

Accepted Answer

A)  $2 / 3$ 
B)  $6 / 7$ 
C)  $5 / 6$ 
D)  $4 / 5$ 
A)  $2 / 3$ 
B)  $6 / 7$ 
C)  $5 / 6$ 
D)  $4 / 5$

Question 19

A school is sending 9 children to a camp. If 15% of the children in the school are first graders, and the 8
children are selected at random, what is the mean and variance of the number of first graders chosen?

Accepted Answer

The mean i

The sum of the probabilities of all the events in the sample space must equal 1.

Discrete variables have values that can be measured.

{ Find the mean of the distribution shown. -4 -2 0 2 () 0.17 0.24 0.50 0.09

If the standard deviation of a probability distribution is 1.71, the variance is 1.31.

Using the multinomial formula, find the probability of the following data.

Find the mean of the distribution shown . 1 2 () 0.48 0.52

Without writing down any calculations, determine the mean of the distribution shown. The variance of this probability distribution is (you can do this in your head!) -1 0 1 () 0.25 0.50 0.25

In a binomial experiment, the outcomes of each trial must be dependent on each other.

A(n) probability distribution consists of the values a random variable can assume and the corresponding probabilities of the values. ______________________________

The supervisor at a large plant estimates that there are defective parts about 1% of the time. If the plant produces 20,000 parts in a week, what is the variance for the number of defective parts?

The probability that federal income tax returns will have 0, 1, or 2 errors is 0.53, 0.15, and 0.32, respectively. If 10 randomly selected returns are audited, what is the probability that six will have no Errors, three will have one error, and one will have two errors?

Using the formula for the multinomial distribution, the probability of $X _ { 1 } = 2 , X _ { 2 } = 1 , X _ { 3 } = 2$ when $\mathrm { n } = 5$ , $\mathrm { p } _ { 1 } = 0.4 , \mathrm { p } _ { 2 } = 0.5 , \mathrm { p } _ { 3 } = 0.1$ is

What probability value would be needed to complete the following probability distribution? -5 -1 0 1 4 () 0.09 0.24 0.16 0.27

What of the following pairs of probability values would complete the following probability distribution? -3 -2 -1 0 1 2 () 0.09 0.18 0.14 0.23

One of the requirements for a binomial experiment is that there must be a number of trials. ______________________________

The figure below represents the probability distribution for selecting a number of objects out of a container. Construct a probability distribution from this graph.

What value would be needed to complete the following probability distribution? x P(x) 0 1/3 1 1/8 2 1/8 3 1/6 4

A package of 10 batteries is checked to determine if there are any dead batteries. Four batteries are checked. If one or more are dead, the package is not sold. What is the probability that the package will Not be sold if there are actually three dead batteries in the package?

A school is sending 9 children to a camp. If 15% of the children in the school are first graders, and the 8 children are selected at random, what is the mean and variance of the number of first graders chosen?

The Nature of Probability and Statistics

Frequency Distributions and Graphs

Data Description

The Normal Distribution

Confidence Intervals and Sample Size

Hypothesis Testing

Testing the Difference Between Two Means, Two Proportions, and Two Variances

Correlation and Regression

Chi-Square and Analysis of Variance Anova

Tables

Data Bank

Glossary

Filters

Exam 4: Discrete Probability Distributions

The sum of the probabilities of all the events in the sample space must equal 1.

Discrete variables have values that can be measured.

{ Find the mean of the distribution shown. -4 -2 0 2 () 0.17 0.24 0.50 0.09

If the standard deviation of a probability distribution is 1.71, the variance is 1.31.

Using the multinomial formula, find the probability of the following data.

Find the mean of the distribution shown . 1 2 () 0.48 0.52

Without writing down any calculations, determine the mean of the distribution shown. The variance of this probability distribution is (you can do this in your head!) -1 0 1 () 0.25 0.50 0.25

In a binomial experiment, the outcomes of each trial must be dependent on each other.

A(n) __________ probability distribution consists of the values a random variable can assume and the corresponding probabilities of the values. ________________________________________

The supervisor at a large plant estimates that there are defective parts about 1% of the time. If the plant produces 20,000 parts in a week, what is the variance for the number of defective parts?

The probability that federal income tax returns will have 0, 1, or 2 errors is 0.53, 0.15, and 0.32, respectively. If 10 randomly selected returns are audited, what is the probability that six will have no Errors, three will have one error, and one will have two errors?

What probability value would be needed to complete the following probability distribution? -5 -1 0 1 4 () 0.09 0.24 0.16 0.27

What of the following pairs of probability values would complete the following probability distribution? -3 -2 -1 0 1 2 () 0.09 0.18 0.14 0.23

One of the requirements for a binomial experiment is that there must be a __________ number of trials. ________________________________________

The figure below represents the probability distribution for selecting a number of objects out of a container. Construct a probability distribution from this graph.

What value would be needed to complete the following probability distribution? x P(x) 0 1/3 1 1/8 2 1/8 3 1/6 4

A package of 10 batteries is checked to determine if there are any dead batteries. Four batteries are checked. If one or more are dead, the package is not sold. What is the probability that the package will Not be sold if there are actually three dead batteries in the package?

A school is sending 9 children to a camp. If 15% of the children in the school are first graders, and the 8 children are selected at random, what is the mean and variance of the number of first graders chosen?

The Nature of Probability and Statistics

Frequency Distributions and Graphs

Data Description

The Normal Distribution

Confidence Intervals and Sample Size

Hypothesis Testing

Testing the Difference Between Two Means, Two Proportions, and Two Variances

Correlation and Regression

Chi-Square and Analysis of Variance Anova

Tables

Data Bank

Glossary

Filters

A(n) probability distribution consists of the values a random variable can assume and the corresponding probabilities of the values. ______________________________

One of the requirements for a binomial experiment is that there must be a number of trials. ______________________________