1. The heights of eighteen-year-old women are approximately normally distributed with mean 64 inches and standard deviation 2 inches. Answer the following questions showing all steps.

a. Calculate the probability that one randomly selected eighteen-year-old woman will be more than 65 inches tall.

b. A random sample of 9 eighteen-year-old women is selected and the mean height of the sample, x is calculated. Determine the mean and the standard deviation of the sampling distribution of x. (Round to two decimal places if necessary.) Is this distribution normal? Explain how you can tell.