It can be shown that a sum of normally distributed random variables is also normally distributed. Do all functions of normal random variables lead to normal random variables?
Consider the following. Super Drugs is a chain of drugstores with three similar size stores in a given city. The sales in a given week for any of these stores is normally distributed with mean $15,000 and standard deviation $3000.
At the end of each week, the sales figure for the store with the largest sales among the three stores is recorded.
Is this maximum value normally distributed? To answer this question, simulate a weekly sales figure at each of the three stores and calculate the maximum. Then replicate this maximum 500 times and create a histogram of the 500 maximum values.
Does it appear to be normally shaped? Whatever this distribution looks like, use your simulated values to estimate the mean and standard deviation of the maximum.