•Result Summary

There are several trends to notice here:

First, the difference between σ and becomes less noticeable as your sample size gets larger.

Second, the mean of a sum of randrom numbers gets bigger much faster than the standard deviation does.  That means that typically these histograms get narrower as the number of items in the population gets bigger.  

Third, for say 20 dice even a good computer will crap out: is just too big.  So either we find a way to get what we want analytically (which is pretty straightforward for a situation as simple as dice goes), or we sample the population, and estimate things from that sample.  

Converted by Mathematica  (September 11, 2003)