Question

Suppose the heights of 18-year-old men are approximately normally distributed, with mean 71 inches and standard deviation 4 inches. If a random sample of twenty-eight 18-year-old men is selected, what is the probability that the mean height x is between 70 and 72 inches?

Answer 1

Solution:-

Given data:

Mean, = 71 inches

Standard deviation, = 4 inches

Number of random samples, n = 28

Here we have to calculate the probability that the mean height x is between 70 and 72 inches.

i.e, required probability is

.

Hence, the probability that the mean height x is between 70 and 72 inches is 0.8132.