Question

Assume that military aircraft use ejection seats designed for men weighing between 138.4 lb and 211 lb. If​ women's weights are normally distributed with a mean of 174.8 lb and a standard deviation of 42.1 ​lb, what percentage of women have weights that are within those​ limits? Are many women excluded with those​ specifications?

Answer 1

mean = 174.8

sd = 42.1

P(138.4 < x < 211)

z value for x = 138.4

z = -0.8646 = -0.86

z value for x = 211

z = 0.8599 = 0.86

P(-0.86 < z < 0.86)

P (−0.86 < Z < 0.86 )=P ( Z < 0.86 )−P (Z < −0.86 )

P ( Z < 0.86 )=0.8051

P ( Z<−0.86)=1−P ( Z < 0.86 )=1−0.8051=0.1949

P (−0.86<Z<0.86 )=0.6102

ANS: 61.02% of women are within those limits. 38.98%, almost 40% of the women are excluded with those specifications.