Fill in the missing value so that the following table represents a probability distribution. $\begin{array}{c|cccl} x & -4 & -3 & -2 & -1 \\ \hline P(x) & 0.42 & 0.08 & ? & 0.05 \end{array}$

A) 0.26 B) 0.45 C) 0.33 D) 0.25 A) 0.26 B) 0.45 C) 0.33 D) 0.25

\[\begin{array}{l} \text { Find the mean of the distribution shown below. }\\ \begin{array} { l | c c c } \boldsymbol { X } & 2 & 3 & 4 \\ \hline \boldsymbol { P } ( \boldsymbol { X } ) & 0.26 & 0.31 & 0.43 \end{array} \end{array}\]

A) 1.67 B) 2.17 C) 3.17 D) 2.67 A) 1.67 B) 2.17 C) 3.17 D) 2.67

\[\begin{array}{l} \text { Find the mean of the distribution shown. }\\ \begin{array} { l | c c } \boldsymbol { X } & 1 & 2 \\ \hline \boldsymbol { P } ( \boldsymbol { X } ) & 0.32 & 0.68 \end{array} \end{array}\]

A) 1.17 B) 0.50 C) 1.50 D) 1.68 A) 1.17 B) 0.50 C) 1.50 D) 1.68

\[\begin{array}{l} \text { Compute the mean of the random variable with the given discrete probability distribution. }\\ \begin{array} { c c } \hline x & P ( x ) \\ \hline 0 & 0.45 \\ 15 & 0.05 \\ 20 & 0.5 \\ 30 & 0 \\ \hline \end{array} \end{array}\]

A) 10.75 B) 9.8 C) 95.7 D) 16.25 A) 10.75 B) 9.8 C) 95.7 D) 16.25

\[\begin{array}{l} \text { Find the mean of the distribution shown. }\\ \begin{array} { l | c c } \boldsymbol { X } & 4 & 6 \\ \hline \boldsymbol { P } ( \boldsymbol { X } ) & 0.47 & 0.53 \end{array} \end{array}\]

A) 1.53 B) 5.06 C) 6.00 D) 4.00 A) 1.53 B) 5.06 C) 6.00 D) 4.00

\[\begin{array}{l} \text { The following distribution is $\underline{\text { not }}$ a probability distribution because }\\ \begin{array} { l | c c c c c } \boldsymbol { X } & - 2 & - 1 & 0 & 1 & 2 \\ \hline \boldsymbol { P } ( \boldsymbol { X } ) & 0.16 & 0.15 & 0.42 & 0.13 & 0.31 \end{array} \end{array}\]

A) the probability values are not increasing. B) the probability values are not discrete. C) the values of the variable are negative. D) the probability values do not add to 1. A) the probability values are not increasing. B) the probability values are not discrete. C) the values of the variable are negative. D) the probability values do not add to 1.

The number of cartoons watched on Saturday mornings by students in Mrs. Kelly's first $g$ | class is shown below. $\begin{array} { l l l l l l l } \text { Number of cartoons watched } \boldsymbol { X } & 0 & 1 & 2 & 3 & 4 & 5 \\ \text { Probability } \boldsymbol { P } ( \boldsymbol { X } ) & 0.15 & 0.20 & 0.30 & 0.10 & 0.20 & 0.05 \end{array}$ Give the standard deviation for the probability distribution. de

A) 1.46 B) 1.89 C) 1.18 D) 2.25 A) 1.46 B) 1.89 C) 1.18 D) 2.25

Exam 5: Discrete Probability Distributions

A computer store has 75 printers of which 25 are laser printers and 50 are ink jet printers. If a group of 10 printers is chosen at random from the store, find the mean and variance Of the number of ink jet printers.

(Multiple Choice)

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Question 81

A school is sending 12 children to a camp. If 20% of the children in the school are first graders, and the 12 children are selected at random from among all 6 grades at the school, find the mean and variance of the number of first graders chosen?

(Short Answer)

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Question 82

A die is rolled 360 times. Find the standard deviation of the number of times a 3 will be rolled.

(Multiple Choice)

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Question 83

The number of typographical errors in a document follows a Poisson distribution with a mean of 3 errors per page. Let $X$ represent the number of errors on 4 pages. Find $\mu _ { x }$ .

(Multiple Choice)

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Question 84

Fill in the missing value so that the following table represents a probability distribution. x -4 -3 -2 -1 P(x) 0.42 0.08 ? 0.05

(Multiple Choice)

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Question 85

Find the mean of the distribution shown below. 2 3 4 ( ) 0.26 0.31 0.43

(Multiple Choice)

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Question 86

In a batch of 100 cell phones, there are, on average, 6 defective ones. If a random sample of 25 is selected, find the probability of 3 defective ones.

(Multiple Choice)

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Question 87

In a survey, 65% of the voters support a particular referendum. If 20 voters are chosen at random, find the standard deviation of the number of voters who support the referendum.

(Short Answer)

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Question 88

Find the mean of the distribution shown. 1 2 ( ) 0.32 0.68

(Multiple Choice)

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Question 89

The binomial distribution equations will not give exact probabilities for experiments in which sampling is done without replacement. In those cases, the trials are not independent.

(True/False)

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Question 90

Compute the mean of the random variable with the given discrete probability distribution. x P(x) 0 0.45 15 0.05 20 0.5 30 0

(Multiple Choice)

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Question 91

The following table presents the probability distribution of the number of vacations $X$ taken last year for a randomly chosen family. Find the probability that a family took at lea vacations last year. x 0 1 2 3 4 P(x) 0.05 0.69 0.17 0.07 0.02

(Multiple Choice)

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Question 92

A certain type of battery has a 0.5% failure rate. Find the probability that a shipment of 1,000 batteries has more than two defective batteries.

(Multiple Choice)

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Question 93

Compute the standard deviation of the random variable with the given discrete probability distribution. x P(x) 0 0.2 5 0.45 15 0.05 25 0.3

(Multiple Choice)

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Question 94

Find the mean of the distribution shown. 4 6 ( ) 0.47 0.53

(Multiple Choice)

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Question 95

Determine the indicated probability for a binomial experiment with the given number of trials $n$ and the given success probability $p$ . $n = 7 , p = 0.9 , P ( \text { Fewer than } 4 )$

(Multiple Choice)

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Question 96

Last year, a manufacturer produced 1,450,000 DVD players. Of these, approximately were defective. Assume that a simple random sample of $n = 120$ players is drawn. Use the Poisson approximation to the binomial distribution to compute the mean number of DVD players that were defective.

(Multiple Choice)

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Question 97

The following distribution is a probability distribution because -2 -1 0 1 2 ( ) 0.16 0.15 0.42 0.13 0.31

(Multiple Choice)

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Question 98

The number of cartoons watched on Saturday mornings by students in Mrs. Kelly's first $g$ | class is shown below. Number of cartoons watched 0 1 2 3 4 5 Probability ( ) 0.15 0.20 0.30 0.10 0.20 0.05 Give the standard deviation for the probability distribution. de

(Multiple Choice)

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Question 99

An investor is considering a $25,000 investment in a start-up company. She estimates that she has probability 0.05 of a $15,000 loss, probability 0.15 of a $20,000 loss, Probability 0.35 of a $35,000 profit, and probability 0.45 of breaking even (a profit of $0)) What is the expected value of the profit?

(Multiple Choice)

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Question 100

A computer store has 75 printers of which 25 are laser printers and 50 are ink jet printers. If a group of 10 printers is chosen at random from the store, find the mean and variance Of the number of ink jet printers.

A school is sending 12 children to a camp. If 20% of the children in the school are first graders, and the 12 children are selected at random from among all 6 grades at the school, find the mean and variance of the number of first graders chosen?

A die is rolled 360 times. Find the standard deviation of the number of times a 3 will be rolled.

The number of typographical errors in a document follows a Poisson distribution with a mean of 3 errors per page. Let $X$ represent the number of errors on 4 pages. Find $\mu _ { x }$ .

Fill in the missing value so that the following table represents a probability distribution. x -4 -3 -2 -1 P(x) 0.42 0.08 ? 0.05

Find the mean of the distribution shown below. 2 3 4 ( ) 0.26 0.31 0.43

In a batch of 100 cell phones, there are, on average, 6 defective ones. If a random sample of 25 is selected, find the probability of 3 defective ones.

In a survey, 65% of the voters support a particular referendum. If 20 voters are chosen at random, find the standard deviation of the number of voters who support the referendum.

Find the mean of the distribution shown. 1 2 ( ) 0.32 0.68

The binomial distribution equations will not give exact probabilities for experiments in which sampling is done without replacement. In those cases, the trials are not independent.

Compute the mean of the random variable with the given discrete probability distribution. x P(x) 0 0.45 15 0.05 20 0.5 30 0

The following table presents the probability distribution of the number of vacations $X$ taken last year for a randomly chosen family. Find the probability that a family took at lea vacations last year. x 0 1 2 3 4 P(x) 0.05 0.69 0.17 0.07 0.02

A certain type of battery has a 0.5% failure rate. Find the probability that a shipment of 1,000 batteries has more than two defective batteries.

Compute the standard deviation of the random variable with the given discrete probability distribution. x P(x) 0 0.2 5 0.45 15 0.05 25 0.3

Find the mean of the distribution shown. 4 6 ( ) 0.47 0.53

Determine the indicated probability for a binomial experiment with the given number of trials $n$ and the given success probability $p$ . $n = 7 , p = 0.9 , P ( \text { Fewer than } 4 )$

Last year, a manufacturer produced 1,450,000 DVD players. Of these, approximately were defective. Assume that a simple random sample of $n = 120$ players is drawn. Use the Poisson approximation to the binomial distribution to compute the mean number of DVD players that were defective.

The following distribution is a probability distribution because -2 -1 0 1 2 ( ) 0.16 0.15 0.42 0.13 0.31

The number of cartoons watched on Saturday mornings by students in Mrs. Kelly's first $g$ | class is shown below. Number of cartoons watched 0 1 2 3 4 5 Probability ( ) 0.15 0.20 0.30 0.10 0.20 0.05 Give the standard deviation for the probability distribution. de

The Nature of Probability and Statistics

Frequency Distributions and Graphs

Data Description

Probability and Counting Rules

The Normal Distribution

Confidence Intervals and Sample Size

Hypothesis Testing

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

Correlation and Regression

Other Chi-Square Tests

Analysis of Variance

Nonparametric Statistics

Sampling and Simulation

Filters

Exam 5: Discrete Probability Distributions

A computer store has 75 printers of which 25 are laser printers and 50 are ink jet printers. If a group of 10 printers is chosen at random from the store, find the mean and variance Of the number of ink jet printers.

A school is sending 12 children to a camp. If 20% of the children in the school are first graders, and the 12 children are selected at random from among all 6 grades at the school, find the mean and variance of the number of first graders chosen?

A die is rolled 360 times. Find the standard deviation of the number of times a 3 will be rolled.

The number of typographical errors in a document follows a Poisson distribution with a mean of 3 errors per page. Let XXX represent the number of errors on 4 pages. Find μx\mu _ { x }μx​ .

Fill in the missing value so that the following table represents a probability distribution. x -4 -3 -2 -1 P(x) 0.42 0.08 ? 0.05

Find the mean of the distribution shown below. 2 3 4 ( ) 0.26 0.31 0.43

In a batch of 100 cell phones, there are, on average, 6 defective ones. If a random sample of 25 is selected, find the probability of 3 defective ones.

In a survey, 65% of the voters support a particular referendum. If 20 voters are chosen at random, find the standard deviation of the number of voters who support the referendum.

Find the mean of the distribution shown. 1 2 ( ) 0.32 0.68

The binomial distribution equations will not give exact probabilities for experiments in which sampling is done without replacement. In those cases, the trials are not independent.

Compute the mean of the random variable with the given discrete probability distribution. x P(x) 0 0.45 15 0.05 20 0.5 30 0

The following table presents the probability distribution of the number of vacations XXX taken last year for a randomly chosen family. Find the probability that a family took at lea vacations last year. x 0 1 2 3 4 P(x) 0.05 0.69 0.17 0.07 0.02

A certain type of battery has a 0.5% failure rate. Find the probability that a shipment of 1,000 batteries has more than two defective batteries.

Compute the standard deviation of the random variable with the given discrete probability distribution. x P(x) 0 0.2 5 0.45 15 0.05 25 0.3

Find the mean of the distribution shown. 4 6 ( ) 0.47 0.53

Determine the indicated probability for a binomial experiment with the given number of trials nnn and the given success probability ppp . n=7,p=0.9,P( Fewer than 4)n = 7 , p = 0.9 , P ( \text { Fewer than } 4 )n=7,p=0.9,P( Fewer than 4)

Last year, a manufacturer produced 1,450,000 DVD players. Of these, approximately were defective. Assume that a simple random sample of n=120n = 120n=120 players is drawn. Use the Poisson approximation to the binomial distribution to compute the mean number of DVD players that were defective.

The following distribution is a probability distribution because -2 -1 0 1 2 ( ) 0.16 0.15 0.42 0.13 0.31

The number of cartoons watched on Saturday mornings by students in Mrs. Kelly's first ggg | class is shown below. Number of cartoons watched 0 1 2 3 4 5 Probability ( ) 0.15 0.20 0.30 0.10 0.20 0.05 Give the standard deviation for the probability distribution. de

The Nature of Probability and Statistics

Frequency Distributions and Graphs

Data Description

Probability and Counting Rules

The Normal Distribution

Confidence Intervals and Sample Size

Hypothesis Testing

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

Correlation and Regression

Other Chi-Square Tests

Analysis of Variance

Nonparametric Statistics

Sampling and Simulation

Filters

The number of typographical errors in a document follows a Poisson distribution with a mean of 3 errors per page. Let $X$ represent the number of errors on 4 pages. Find $\mu _ { x }$ .

The following table presents the probability distribution of the number of vacations $X$ taken last year for a randomly chosen family. Find the probability that a family took at lea vacations last year. x 0 1 2 3 4 P(x) 0.05 0.69 0.17 0.07 0.02

Determine the indicated probability for a binomial experiment with the given number of trials $n$ and the given success probability $p$ . $n = 7 , p = 0.9 , P ( \text { Fewer than } 4 )$

Last year, a manufacturer produced 1,450,000 DVD players. Of these, approximately were defective. Assume that a simple random sample of $n = 120$ players is drawn. Use the Poisson approximation to the binomial distribution to compute the mean number of DVD players that were defective.

The number of cartoons watched on Saturday mornings by students in Mrs. Kelly's first $g$ | class is shown below. Number of cartoons watched 0 1 2 3 4 5 Probability ( ) 0.15 0.20 0.30 0.10 0.20 0.05 Give the standard deviation for the probability distribution. de