Stats homework please help

Question

Decide if the Central Limit Theorem applies in the following situation. Explain.

The mean height of men in the U.S. is 69.6 inches with a standard deviation of 3 inches. A random sample of 35 men are selected. Find the probability that the mean height is less than 70 inches

Answer 1

Because the sample size of >= 30 is selected, we can apply the CLT and assume the sample means are normally distributed with a mean of 69.6 and a standard error of 3/square root(35) = 0.507,

xbar = mean height. want to find P(xbar < 70)

compute standardized z variable = (xbar - population mean)/standard error = (xbar - 69.6/0.507)

So P(xbar < 70) = P(z < (xbar < (70 - 69.6)/0.507) = P(z < 0.79) = 0.7852