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Chapter 2: Q. 41 (page 131)

The distribution of heights of adult American men is approximately Normal with mean 69inches and standard deviation of 2.5inches. Draw a Normal curve on which this mean and standard deviation are correctly located. (Hint: Draw the curve first, locate the points where the curvature changes, then mark the horizontal axis.)

Short Answer

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Here's a simple sketch of the distribution of men's heights based on the explanation below.

Step by step solution

01

Given Information

The American men has approximately mean 69inches and standard deviation 2.5inches.

02

Explanation

Normal distribution's Empirical rule is:

In about 68%of the observations, the mean is within 1standard deviation.

x¯−s=69−2.5=66.5x¯+s=69+2.5=71.5

In about 95% of the observations, the mean is within2standard deviation.

x¯-2s=69-2(2.5)=64x¯+2s=69+2(2.5)=74

In about 99.7%of the observations, the mean is within3standard deviation.

x¯-3s=69-3(2.5)=61.5x¯+3s=69+3(2.5)=76.5

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