Question

Assume that military aircraft use ejection seats designed for men weighing between 132.8 and 209lb. If​ women's weights are normally distributed with a mean of 178.2lb and a standard deviation of 40.3 ​lb, what percentage of women have weights that are within those​ limits? Are many women excluded with those​ specifications?

Answer 1

Women's

Mean = u = 178.2 lb

Std dev. = s = 40.3 lb

limit values => ( 132.8 , 209 )

Z score = ( x - u ) /s

Z( 132.8 ) = ( 132.8 - 178.2)/40.3 = -1.13

Z( 209 ) = ( 209 - 178.2)/40.3 = 0.76

P ( -1.13 < Z < 0.76 ) = 0.6471 = 64.7% of women have weights that are within those​ limits.

Yes, many women are included.