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.
SuperDrugs is a chain of drugstores with three similarsize
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.