Question

In a survey of men in the United States (ages 20-29), the mean height was 69.6 inches with a standard deviation of 3.0 inches. Find the minimum height in the top 22%.

Answer 1

$μ = 69.6 \\ σ = 3.0 \\ P(X<x) = P(Z< \frac{x-69.6}{3.0}) = 1 -0.22 = 0.79 \\ P(Z< \frac{x-69.6}{3.0}) = 0.79 \\ \frac{x-69.6}{3.0} = 0.81 \\ x -69.6 = 2.43 \\ x = 72.03$

The minimum height in the top 22% is 72.03 inches.