Assume that military aircraft use ejection seats designed for men weighing between 141.5 lb and 201 lb. If​ women's weights are normally distributed with a mean of 160.6 lb and a standard deviation of 48.7 ​lb, what percentage of women have weights that are within those​ limits? Are many women excluded with those​ specifications?

Question
Asked Apr 21, 2019

Assume that military aircraft use ejection seats designed for men weighing between 141.5 lb and 201 lb. If​ women's weights are normally distributed with a mean of 160.6 lb and a standard deviation of 48.7 ​lb, what percentage of women have weights that are within those​ limits? Are many women excluded with those​ specifications?

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Step 1

Solution

Given: The military aircraft use ejection seats designed for men weighing between 141.5 lb and 201 lb. Women’s weights are normally distributed with a mean µ = 160.6 and standard deviation σ = 48.7.

Step 1:

To find the percentage of women have weights that are within 141.5lb and 201lb we need to find the z scores corresponding to 141.5 lb and 201lb.

The z score is computed using the formula,

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Step 2

Step 2:

To find the z – score corresponding to 141.5, substitute the values X = 141.5, µ = 160.6, and σ = 48.7 in the formula. We get the z score as

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Step 3

To find the z – score corresponding to 201, substitute the values X = 201, µ = 16...

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