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Chapter 6: Q. 36 (page 378)

A report of the National Center for Health Statistics says that the height of a 20-year-old man chosen at random is a random variable H with mean 5.8feet (ft) and standard deviation0.24 ft. Find the mean and standard deviation of the height J of a randomly selected 20-year-old man in inches. There are 12 inches in a foot

Short Answer

Expert verified

The mean and standard deviation are:

μJ=69.6

σJ=2.88

Step by step solution

01

Given Information

Given

μH=5.8

σH=0.24

1foot =12inches

Since 1foot is also 12inches:

J=12H

02

Explanation

Properties mean and standard deviation

μaX+b=aμX+b

σaX+b=aσX

Then we obtain for J=12H:

localid="1649910916895" μJ=μ12H=12μH=12(5.8)=69.6

localid="1649910931312" σJ=σ12H=12σH=12(0.24)=2.88

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