Question

In a population of 225 women, the heights of the women are normally distributed with a mean of 64.5 inches and a standard deviation of 2.9 inches. If 25 women are selected at a random, find the probability that their mean height will exceed 66 inches. Assume that the sampling is done without replacement and use a finite population correction factor with N=225. Pls. show solution

Answer 1

N = 225

n = 25

=64.5

= 2.9

Finite Population Correction Factor (FPC) is got as follows:

Substituting values, we get:

To find P(>66):
Z = (66 - 64.5)/0.5480 = 2.7370

Table of Area Under Standard Normal Curve gives area = 0.4969

So,

P( > 66) =0.5 - 0.4969 = 0.0031

So,

Answer is:

0.0031