If Air Force only accepts someone who is at top 15%, what is his minimum required height?

Question

If Air Force only accepts someone who is at top 15%, what is his minimum required height?

mean = 70 inches

standard deviation = 2.5 inches

Answer 1

use standardized normal value: z = (x - mean)/std = (x - 70)/2.5

top 15% is the 85th percentile.

for 85th percentile z = 1.04

so 1.04 = (x - 70)/2.5

x = 1.04 * 2.5 + 70 = 72.6