Probability distribution

Question

Assume that the heights of men are normally distributed with a mean of 70 inches and a standard deviation of 3.5 inches. If 100 men are randomly selected, find the probability that they have a mean height greater than 71 inches.

Answer 1

The z-score is (71-70)/ ( 3.5/ sqrt(100)) =

1 / (3.5/10) =

1/ 0.35 = 100/35 = 20/7 = 2 and 6/7

So Prob (z > 2 and 6/7) = 1 - Prob ( z< 2 and 6/7) = 1 - 0.997814 = 0.2186%