Question

Assume that military aircraft use ejection seats designed for men weighing between

134

lb and

200

lb. If​ women's weights are normally distributed with a mean of

164.6

lb and a standard deviation of

48.2

​lb, what percentage of women have weights that are within those​ limits? Are many women excluded with those​ specifications?

Answer 1

P(134 < X < 200)
= P((134 - 164.6)/48.2 < z < (200 - 164.6)/48.2)
= P(-0.63   < z < 0.73)
= P(z < 0.73) - P(z < -0.63)
= 0.7673 - 0.2643
= 0.503

Hence 50.3% of women are within the limit and 49.7% excluded with those specifications.