Binomial and Normal Distributions Compared

Statistics - investigating the conditions for the continuous Normal distribution to be used as an approximation to the discrete Binomial distribution using a continuity correction.

Author and programmer: Ron Barrow

Instructions below    See also:    Binomial and Poisson   Poisson and Normal    Binomial Expansions    PRINT

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How to Use this Applet

This applet is designed to help you to visualise the shape of Binomial distributions, and the effect of varying the parameters n and p. By clicking and dragging the two sliders at the bottom, n can be varied from 2 to 100, and p from 0.01 to 0.99. You can see the values of different Binomial probabilities near the bottom of the screen, and you can change the range you want by sliding the black balls along the baseline of the graph. Try it out for yourself. Checking "Normal" box draws, in yellow, the pdf (probability density function) of the Normal distribution which has the same mean and variance as the Binomial. It also displays some Normal probabilities to help you compare with the Binomial ones. A percentage error is also shown. Each distribution can be clicked on or off, to help you compare the two distributions. Clicking "Reset" returns the screen to the starting position. Play around with different numbers of trials (n) and different probabilities of success (p). You should try to judge when one distribution is a good approximation of the other, and when it isn't. Learn by experimenting. If you check the "Rectangles" box, the Binomial 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 approximate Binomial probabilities.