   Chapter 8, Problem 5T ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# For the probability distribution shown, find the mean, variance, and standard deviation. x 10 12 15 18 20 25 Pr(x) 0.1 0.3 0.1 0.2 0.1 0.2

To determine

To calculate: The mean, variance and standard deviation of the variable x for the probability distribution given in the table.

x101215182025Pr(x)0.10.30.10.20.10.2

Explanation

Given Information:

The probability distribution given in the table.

x101215182025Pr(x)0.10.30.10.20.10.2

Formula used:

The mean or Expected value is,

E(x)=xPr(x)

The Variance is,

σ2=(xμ)2Pr(x)

The standard deviation is,

σ=variance

Calculation:

From the table,

x101215182025Pr(x)0.10.30.10.20.10.2

Expected value will be,

μ=10Pr(10)+12Pr(12)+xPr(x)+15Pr(15)+18Pr(18)+20Pr(20)+25Pr(25)=10(0.1)+12(0.3)+15(0.1)+18(0.2)+20(0.1)+25(0.2)=1+3.6+1.5+3.6+2+5=16.7

Now, variance is calculated as,

σ2={(1016

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