Question

Men’s heights are normally distributed with a mean of 71.8 inches and a standard deviation of 3.4 inches. A social organization for short people has a requirement that men must be at most 65 inches tall. What percentage of men meet this requirement?

Answer 1

Answer: 2.28%

Explanation:

μ = 71.8

σ = 3.4

X < 65

P(X < 65) = P (Z < 65 - 71.8/3.4) = P (Z < -2)

According to the table for the normal distribution attached, it will give us

P (z < Z < 0), this way, to find the P(Z < z), we need to do 0.5 - P:

0.5 - P(-2 < Z < 0) = 0.5 - 0.4772 = 0.0228

In percentage: 0.0228*100 = 2.28%