Question

Assume that the heights of men are normally distributed with a mean of 67.9 inches and a standard deviation of 2.1 inches. If 36 men are ramdomly selectd, find theprobability that they have a mean height greater than 68.9 inches.

Answer 1

μ = 67.9

σ = 2.1

n = 36

xbar = 68.9 = sample mean

We were given population standard deviation so we can use z distribution

P(xbar>68.9) = P((xbar-μ)/(σ/√n) > (68.9-67.9)/(2.1/√36)) = P(z > 2.86) = .0021