# The Central Limit Theorem

The central limit theorem explains why many distributions tend to be close to the normal distribution.
The key ingredient is that the random variable being observed should be the sum or mean of many independent
identically distributed random variables. One version of the theorem is

In this applet, we look at rolling dice again. Let **X** be the number of
spots showing when one die is rolled.
The mean value for
rolling one die is 3.5, and the variance is .
If **S**_{n} is the number of spots showing when *n* dice are rolled,
then if *n* is ``large'' the random variable

should be approximately standard normal, so **S**_{n} itself should be
approximately normal with mean 3.5**n* and variance 35*n*/12.
The red curve is the graph of the density function with these parameters.

### Source Code

This applet uses the Danby package in additon to the following
java files: