An Illustration of Basic Probability: The Normal Distribution

The normal (or Gaussian) distribution is one of the most commonly observed and is the starting point for modeling many natural processes. It usually is found in events that are the aggregation of many smaller, but independent (may be unobservable) random events.

The applet below illustrates a simple process that gives rise to the familiar "bell curve" of the normal distribution. In this case balls are dropped from the top and pass through a series of pins until they hit the bottom. Once at the bottom, they stack up to record the number that have hit that point. At first there does not seem to be any pattern but after a few minutes the stacks conform to the superimposed curve.

This idea of illustration goes back to Sir Francis Galton (1822-1911). Why does it work? Well, the final position of each ball is determined by many (here only 8) independent, random events of whether to drop to the left or the right of the pin, thus the (approximate) normal distribution.

Incidentally the German 10 Mark note has Karl F. Gauss printed on the back, and a small bell shaped curve and its math formula in the background, below the letter C.

K.F. Gauss

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original applet written by David Krider
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