Suppose someone notices that in his sample of 30 supposedy normal data points, the highest 
point is 0.5 standard deviations above the next highest.  That gap, he claims, is unusual.  Now we
can be sure that the probability that the highest two in a normal sample of 30 will differ by more 
than 0.5 standard deviations is not a function of how big the true standard deviation is, nor is it 
a function of the mean. Thus we can study just N(0,1) data to get the distribution of this gap. 
I am interested in the mean gap (in units of standard deviation) and the 5th and 95th percentile 
(after all , the top two could also possibly be too close together). 



Simulate 10,000 of these gaps and use PROC UNIVARIATE to get the percentiles.  Make a note
of the mean and the  5th and 95th percentiles (highlight or circle them for example).  As you run 
your simulations, make a variable X that is 0 if the gap is less than 0.5 and 1 otherwise.  Compute
the mean of this variable using PROC MEANS.  Why are we interested in that mean?  Note that 
these are Bernoulli trials (0,1).  The mean and variance of such trials are related, as we learn in 
stat classes. What is the variance implied by the mean of X and what is the variance estimated 
by PROC MEANS? (any non-stat majors can skip that last part) 



If you get stuck on this, the program IML3.SAS will be of help.  Please try it on your own first. 
If you use a modification of IML3, then at least explain that portion of the program that uses the
rank[   ] function. You will need to change a couple of other features as well.  This will be our last
assignment.