Question

Assume that military aircraft use ejection seats designed for men weighing between 136.3 Ib and 213 Ib. If women's weights are normally distributed with a mean of 176.3 Ib and a standard deviation of 40.5 Ib., what percentage of women have weights that are within those limits? Are many women excluded with those specifications?

The percentage of women that weights between those limits is:

Answer 1

Solution :

Given that ,

mean = = 176.3

standard deviation = = 40.5

P(136.3 < x < 213) = P[(136.3 - 176.3)/ 40.5) < (x - ) /  < (213 - 176.3) / 40.5) ]

= P(-0.99 < z < 0.91)

= P(z < 0.91) - P(z < -0.99)

Using z table,

= 0.8186 - 0.1611

= 0.6575

The percentage of women that weights between those limits is: 65.75%

Yes, the percentage of women who are excluded, which is equal to the complement of the probability found previously, shows that about half of the women are excluded.