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Chapter 6: Q. 35 (page 378)

The length in inches of a cricket chosen at random from a field is a random variable Xwith mean 1.2inches and standard deviation of 0.25 inches. Find the mean and standard deviation of the length Y of a randomly chosen cricket from the field in centimeters. There are 2.54 centimeters in an inch.

Short Answer

Expert verified

The mean and standard deviation are:

μY=3.048

σY=0.635

Step by step solution

01

Given Information

Given

μX=1.2

σX=0.25

2.5cm=1inch

Since 1inch is also 2.54cm:

Y=2.54X

02

Explanation

Properties mean and standard deviation:

μaX+b=aμX+b

σaX+b=aσX

Then we obtain for Y=2.54X:

localid="1649911083440" μY=μ2.54X=2.54μX=2.54(1.2)=3.048

localid="1649911096910" σY=σ2.54X=2.54σX=2.54(0.25)=0.635

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