Question

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

148.1 lb and 208 lb. If​ women's weights are normally distributed with a mean of

177.9 lb and a standard deviation of 42.2 ​lb, what percentage of women have weights that are within those​ limits? Are many women excluded with those​ specifications?

Answer 1

Solution :

Let X be a random variable which represents the women's weights.

Given that, X ~ N(177.9, 42.2²)

μ = 177.9 lb and  σ = 42.2 lb

We have to find P(148.1 ≤ X ≤ 208).

P(148.1 ≤ X ≤ 208) = P(X ≤ 208) - P(X < 148.1)

We know that, if X ~ N(μ, σ²), then

Using "pnorm" function of R we get,

P(Z ≤ 0.7133) = 0.7621 and P(Z < -0.7062) = 0.2400

Hence, 52.21% of women have weights that are within those​ limits.

Approximately (100% - 52.21%) = 47.79% of women excluded with those specifications.