In a population of 240 women,the heights of the women are normally distributed with a mean of 64.2 inches and a standard deviation of 3.2 inches. If 36 women are selected at random, find the mean mu x and stand deviation sigma x of the population of sample means. Assume that the sampling is done without replacement and use a finite population correction factor.

A)64.2in,0.49in
B)64.2in,1.88in
C)59.3in,2.96in
D)64.2in,3.2in

Please show work

To find the mean (μx) and standard deviation (σx) of the population of sample means, we can use the formulas:

μx = μ (Mean of the original population)
σx = σ / √n * √(N - n)/(N - 1) (Standard deviation of the sample means)

Given:
Mean of the original population (μ) = 64.2 inches
Standard deviation of the original population (σ) = 3.2 inches
Sample size (n) = 36
Total population size (N) = 240

Now, let's calculate μx and σx.

μx = μ = 64.2 inches (Mean of the original population)

σx = σ / √n * √(N - n)/(N - 1)

Substituting the given values:
σx = 3.2 / √36 * √(240 - 36)/(240 - 1)
= 3.2 / √36 * √204/239
≈ 3.2 / 6 * √0.8536
≈ 0.5333 * 0.9249
≈ 0.4926 inches

The mean (μx) is still the same as the mean of the original population, which is 64.2 inches.

Therefore, the answer is A) 64.2 inches, 0.49 inches.