Men’s heights are normally distributed with a mean of 69.5 inches and standard d
ID: 3266424 • Letter: M
Question
Men’s heights are normally distributed with a mean of 69.5 inches and standard deviation 2.3 inches. The U.S. Navy requires that fighter pilots have heights between 64in. and 75 in.
a. Find the percentage of men that are too short to become fighter pilots.
b. If the Navy changes the height requirements so that all men are eligible except the shortest 5% and the tallest 5%, what are the new height requirements for men?
c. If the Navy changes the height requirements so that all men whose heights fall within the middle 85% of the population are eligible to be fighter pilots, what are the new requirements for men?
Explanation / Answer
a) probability of men that are too short to become fighter pilots=P(X<64)=P(Z<(64-69.5)/2.3)=P(Z<-2.3913)
=0.0084
therefore percentage of men that are too short to become fighter pilots =0.84%
b)for 5% cutoff; z=1.645
therefore shortest eligible height =mean -z*std deviation =65.72
tallest eligible height =mean +z*std deviation =73.28
c)for middle 85% ; z=1.4395
therefore shortest eligible height =mean -z*std deviation =66.19
tallest eligible height =mean +z*std deviation =72.81