Question

Assume that military aircraft use ejection seats designed for men weighing between 136.7 lb and 206 lb. If women's weights are normally distributed with a mean of 160.6 lb and standard deviation of 45.7 lb, what percentage of women have weights that are within those limits? are many women ecluded with those specifations?

Answer 1

Solution :

Given that ,

mean = = 160.6

standard deviation = = 45.7

P(136.7 < x < 206) = P[(136.7-160.6)/45.7 ) < (x - ) /  < (206-160.6-) /45.7 ) ]

= P( -0.52 < z < 0.99)

= P(z < 0.99) - P(z <-0.52 )

= 0.8389 - 0.3015 = 0.5374 ,   Percentages = 53.74%