Assume that military aircraft use ejection seats ?

Question

Assume that military aircraft use ejection seats designed for men weighing between 138.9 lb and 203 lb. If​ women's weights are normally distributed with a mean of 171.8 lb and a standard deviation of 44.9 ​lb, what percentage of women have weights that are within those​ limits? Are many women excluded with those​ specifications?

Answer 1

Explanation :

Given

Mean =μ=171.8

Standard deviation =σ=44.9

To find

P(138.9<X<203)=?

P(138.9<X<203)=P((138.9-171.8)/44.9<X-μ/σ<(203-171.8)/44.9)

Where Z=X-μ/σ

P(138.9<X<203)=P(-0.73<Z<0.69)

Use the standard normal table to conclude that:

P(-0.73<Z<0.69)=0.5222

Hence,

P(138.9<X<203)=0.5222