The heights of American women ages 18 to 24 are normally distributed with a mean of 65 inches and a

Question

standard deviation of 2.5 inches. In order to serve in the U.S. Army, women must be between 58 inches and 80 inches tall. What percentage of women are ineligible to serve based on their height?

 

I got 26% but I do not feel like this is correct

Answer 1

z= (x-μ)/σ = (58-65)/2.5 = -2.8 with left tail p value =0.0026

z= (x-μ)/σ= (80-65)/2.5 = 6 with left tail p value =1

P(x<58) +P(x>80) = 0.0026 +0 = 0.0026=0.26%