Bundle: Understandable Statistics: Concepts And Methods, 12th + Webassign, Single-term Printed Access Card
Bundle: Understandable Statistics: Concepts And Methods, 12th + Webassign, Single-term Printed Access Card
12th Edition
ISBN: 9781337605199
Author: Charles Henry Brase, Corrinne Pellillo Brase
Publisher: Brooks Cole
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Chapter 5.1, Problem 20P

a.

To determine

Calculate the mean, variance, and standard deviation for the given random variable W.

a.

Expert Solution
Check Mark

Answer to Problem 20P

The mean of the random variable W= x1+x2 is μW=118.6 minutes.

The variance of the random variable W= x1+x2 is σW2=298.28.

The standard deviation of the random variable W= x1+x2 is σW17.27 minutes.

Explanation of Solution

Calculation:

Let W be the random variable defined as the total time to examine and repair the computer W= x1+x2 with a=1 and b=1.

Here, x1 is the time to examine computer with mean μ1=28.1 minutes and standard deviation σ1=8.2 minutes and x2 is the time to repair computer with mean μ2=90.5 minutes and the standard deviation σ2=15.2 minutes.

The mean of the random variable is calculated as given below:

μW=μ1+μ2=28.1+90.5=118.6

Thus, the mean of the random variable W= x1+x2 is μW=118.6 minutes.

The variance of the random variable is calculated as given below:

σW2=σ12+σ22=8.22+15.22=298.28

Thus, the variance of the random variable W= x1+x2 is σW2=298.28.

The standard deviation of the random variable is calculated as given below:

σW=σW2=298.2817.27

Thus, the standard deviation of the random variable W= x1+x2 is σW17.27 minutes.

b.

To determine

Calculate the mean, variance, and standard deviation for the given random variable W.

b.

Expert Solution
Check Mark

Answer to Problem 20P

The mean of the random variable W= 1.5x1+2.75x2 is μW=291.03.

The variance of the random variable W= 1.5x1+2.75x2 is σW2=1,898.53.

The standard deviation of the random variable W= 1.5x1+2.75x2 is σW43.57.

Explanation of Solution

Calculation:

Let W be the random variable defined as the service charges W= 1.5x1+2.75x2 with a=1.5 and b=2.75

Here, x1 is the time to examine computer with mean μ1=28.1 minutes and standard deviation σ1=8.2 minutes and x2 is the time to repair computer with mean μ2=90.5 minutes and standard deviation σ2=15.2 minutes.

The mean of the random variable is calculated as given below:

μW=1.5μ1+2.75μ2=1.5(28.1)+2.75(90.5)=291.03

Thus, the mean of the random variable W= 1.5x1+2.75x2 is μW=291.03.

The variance of the random variable is calculated as given below:

σW2=(1.50)2σ12+(2.75)2σ22=2.25(8.2)2+7.5625(15.2)2=1,898.53

Thus, the variance of the random variable W= 1.5x1+2.75x2 is σW2=1,898.53.

The standard deviation of the random variable is calculated as given below:

σW=σW2=1,898.5343.57

Thus, the standard deviation of the random variable W= 1.5x1+2.75x2 is σW43.57.

c.

To determine

Calculate the mean, variance, and standard deviation for the given random variable L.

c.

Expert Solution
Check Mark

Answer to Problem 20P

The mean of the random variable L= 1.5x1+50 is μL=92.15.

The variance of the random variable L= 1.5x1+50 is σL2=151.29.

The standard deviation of the random variable L= 1.5x1+50 is σL12.30.

Explanation of Solution

Calculation:

Let L be the random variable defined as the charges L= 1.5x1+50 with a=50 and b=1.5.

Here, x1 is the time to examine computer with mean μ1=28.1 minutes and standard deviation σ1=8.2 minutes and x2 is the time to repair computer with mean μ2=90.5 minutes and standard deviation σ2=15.2 minutes.

The mean of the random variable is calculated as given below:

μL=50+1.5μ1=50+1.5(28.1)=92.15

Thus, the mean of the random variable L= 1.5x1+50 is μL=92.15.

The variance of the random variable is calculated as given below:

σL2=(1.5)2σ12=2.25(8.2)2=151.29

Thus, the variance of the random variable L= 1.5x1+50 is σL2=151.29.

The standard deviation of the random variable is calculated as given below:

σL=σL2=151.2912.30

Thus, the standard deviation of the random variable L= 1.5x1+50 is σL12.30.

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Chapter 5 Solutions

Bundle: Understandable Statistics: Concepts And Methods, 12th + Webassign, Single-term Printed Access Card

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