Using the procedures in Computer Solutions 8.1 as a general guide, simulate 150 simple random samples of size n = 4 from a normal distribution with a mean of 80 and a standard deviation of 20. Determine the mean and the standard deviation of the 150 sample means, then compare these with their theoretically expected values.
Given the nature of the population distribution, would we expect the distribution of sample means to be at least approximately normally distributed? Generate a histogram of the sample means and comment on the shape of the distribution.