Poisson and Normal Distributions Compared

Statistics - Learn about the Poisson discrete probability distribution and how it can be approximated by the continuous Normal distribution under certain conditions, using continuity corrections.

Author and programmer: Ron Barrow
Author and programmer: Ron Barrow

Instructions below    See also: Binomial and Poisson   Binomial and Normal   The Normal Distribution

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How to Use this Applet

This page is designed to help you visualise Poisson distributions for different values of the parameter (the mean), which can be varied from 1 to 50 using the slider at the bottom. You'll see the Poisson probabilities on a stick graph.
You can compare the Poisson with the Normal distribution with the same mean and variance. The Normal curve can be drawn by selecting the "Normal" checkbox at the bottom.
Clicking "Reset" returns the screen to the starting position. You'll also see the Normal probabilities below.

Play around with different mean values. You should try to visualise when one distribution approximates another, and when it doesn't. Learn by experimenting.
If you check the "Rectangles" box, the Poisson distribution is redrawn with rectangles instead of sticks. This is to help you to understand the need for a continuity correction when you are using the Normal distribution to estimate Poisson probabilities.
Play around!