The Normal Distribution
An Illustration of Basic Probability
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 unobservable events. A good example is the motion of small particles of dust in water.
When viewed in a microscope they perpetually move back and forth from the random impacts of water
molecules. If one were to plot the distance traveled by dust particles over a given time interval
and repeat the measurement several times, the resulting distribution would be normal. The path
followed by the dust particles is referred to as Brownian motion. In this case, the movement of the
dust is the aggregation of several random shocks from the water molecules.
The exhibit below illustrates a more 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.
Galton board used with permission of the author, David Krider.