Answer to Question #202141 in Statistics and Probability for Vichel Vanzuela

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 16%.

Answer 1

$\mu=69.6 \\ \sigma=3.0 \\ P(X>x) = 0.16 \\ P(X<x) = 1-0.16 = 0.84 \\ P(Z< \frac{x-\mu}{\sigma}) = 0.84 \\ \frac{x-69.6}{3.0}=0.995 \\ x-69.6= 3.0 \times 0.995 \\ x = 69.6+2.985 = 72.585$

Answer: 72.58 inches