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.
The exhibit below illustrates 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. Each ball has an equal chance of going left or right after hitting the pins. This means the probability is the same that any ball will fall to one side or the other. Once at the bottom, the balls stack up to show the number that have hit that column or bin. At first there does not seem to be any pattern but after a few minutes the stacks conform to the superimposed normal curve (black line).
The purpose of this demonstration is to show that most processes will follow the normal distribution curve as long as there are no special causes present. In the animation below, we have eliminated special cause. Knowing this gives us the ability to model our process against the normal distribution curve which in turn allows us to detect changes or 'shifts' in our process.
*Clicking on the applet will stop and start the animation