Chapter 5, Problem 5.58LM

Use a statistical software package to generate 100 random samples of size n = 2 from a population characterized by a normal probability distribution with a mean of 100 and a standard deviation of 10. Compute $\bar{x}$ for each sample, and plot a frequency distribution for the 100 values of $\bar{x}$. Repeat this process for n = 5, 10, 30, and 50. How does the fact that the sampled population is normal affect the sampling distribution of $\bar{x}$?