Question

We are given that the average height for women in America is 64 inches tall with a standard deviation of 2.3 inches. Suppose we take a random sample of 31 women from America. Find the probability that the average height of those 31 women falls below 63 inches.

Answer 1

Solution:

Given:  the average height for women in America is 64 inches tall with a standard deviation of 2.3 inches.

Sample Size = n = 31

Since sample size = n = 31 > 30 is large, thus using Central limit theorem, sampling distribution of sample mean follows an approximate Normal distribution with mean of sample means is:

and standard deviation of sample means is:

We have to find: the probability that the average height of those 31 women falls below 63 inches

Find z score:

Thus we get:

Look in z table for z = -2.4 and 0.02 and find area.

P( Z< -2.42 ) = 0.0078

thus