Chapter 9, Problem 79CRE

Women’s Heights Assume women’s heights are approximately Normally distributed with a mean of 65 inches and a standard deviation of $2.5$ inches. Which of the following questions can be answered using the Central Limit Theorem for sample means as needed? If the question can be answered, do so. If the question cannot be answered, explain why the Central Limit Theorem cannot be applied.

Find the probability that a randomly selected woman is less than 63 inches tall.

If five women are randomly selected, find the probability that the mean height of the sample is less than 63 inches.

If 30 women are randomly selected, find the probability that the mean height of the sample is less than 63 inches.