Question

The heights of 18-year-old men are approximately normally distributed with mean 68 inches and standard deviation 3 inches. what is the probability that the average height of a sample of twenty 18-year-old men will be less than 67 inches? round your answer to four decimal places.

Answer 1

The probability is 0.3707.

We calculate the z-score associated with this using the formula 

z = (X-μ)/σ = (67-68)/3 = -1/3 = -0.33

Using a z-table (http://www.z-table.com) we see that the area under the curve to the left of this (less than) is 0.3707.