Question

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

149.6149.6

lb and

212212

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

177.2177.2

lb and a standard deviation of

48.748.7

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

The percentage of women that have weights between those limits is

nothing​%.

​(Round to two decimal places as​ needed.)

Answer 1

Let X denotes the weight of a randomly selected woman.

Here,

X ~ Normal(177.2, 48.72)

The probability that a randomly selected woman is within those​ limits

The percentage of women have weights that are within those​ limits

= 100*P(149.6 < X< 212)

= 100*0.4771

= 47.71%

The percentage of women who do not have weights that are within those​ limits = (100 - 48)% = 52%

Yes, many women are excluded with those​ specifications.