Assume that, among residents of a large (over 6,000) Florida subdivision, the population mean age is 65 years old, the population standard deviation is 2 years, and that the age variable is distributed normally.

a. This question is a continuation of question #3.What is the probability that a sample mean calculated from a sample of 100 individuals from the Florida subdivision will have an average age between 64 and 66 years of age. As in question #3, the mean age of the population is 65 years of age, and the standard deviation is 2 years. (For this problem, be sure to use the z-calculation that is for sample means, and includes the sample size)

b. Is the "normality" assumption for the distribution of ages stated in this question necessary for this question? In other words, is the normality of the "underlying population" a necessary condition for completing this problem? Answer "yes" or "no", and then in a single sentence, state why.