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| Reviewed: |
Feb 02, 2003 by Mathematics |
| Overview: |
The applet graphs the probability distribution functions of the binomial, Poisson and normal distributions. The user may simultaneously display any or all of the probability functions for selected values of n and p. The displayed Poisson and normal distributions have the same mean and variance of the selected binomial distribution. Hence, the applet shows the Poisson and normal approximations to a specified binomial distribution. |
| Learning Goals: |
The applet compares the graphs of the probability functions for the Binomial, Poisson and normal distributions. The applet also shows how accurate the Poisson and normal approximations are to the binomial distribution. It illustrates the DeMoivre-Laplace theorem |
| Target Student Population: |
Students in statistics courses at the high school through undergraduate level. |
| Prerequisite Knowledge or Skills: |
Understanding of the binomial, Poisson and normal distributions. |
| Type of Material: |
Simulation |
| Recommended Uses: |
Classroom demonstration tool, or a supplement to homework activities. |
| Technical Requirements: |
It requires a "Java-enabled" browser. |
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| Strengths: |
The graphs exhibit a smooth transition as changes are made in the parameters n and p of the binomial distribution. By clicking and dragging the two sliders at the bottom, the number of trials (n) can be varied from 2 to 100, and the probability (p) from 0.01 to 0.99 with accuracy to the thousandths place. The graphs are simultaneously displayed as the slider is moved, and the mean and variance for each distribution are displayed.
The user may play around with different numbers of trials (n) and different probabilities of success (p), visualizing when one distribution approximates another, and when it doesn't. |
| Concerns: |
None. |
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Potential Effectiveness as a Teaching Tool |
Rating:   |
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| Strengths: |
The applet is a very effective tool to show the shapes of the binomial, Poisson and normal distributions for corresponding values of n and p and to visually demonstrate the binomial and Poisson approximations to the normal distribution.
The corresponding values for the mean and variance of each distribution are effective in emphasizing the connection between the three distributions.
The immediate display of statistics and curves is extremely effective and allows the user to experiment to the fullest. |
| Concerns: |
It is not possible to select the region of the graphs. Sometimes the graphs are out of bounds.
It would be interesting to have the graphs in another scale or centered in another part.
It is a little difficult to show how the Poisson approaches the binomial distribution for large values of n. The largest possible value of n is 100. Poisson approximations are best for larger values of n and smaller values of p than the ones allowed. |
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Ease of Use for Both Students and Faculty |
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| Strengths: |
It is quite easy to use. The slider bar allows the user to quickly change the values of p and n and determine immediately the effect on each of the three distributions. The explanations are very clear. |
| Concerns: |
None. |
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