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This interactive lab illustrates one of the most
profound and magical facts of statistics, known as the
"Central Limit Theorem". Roughly stated, the Central
Limit Theorem says that, if each of the results of a large number
of independent random events has the same distribution as the
others, then, as the number of events gets large, the
distribution of the *sum* of their results tends toward a
bell-shaped curve (statisticians call this a "normal"
distribution). Amazingly, this fact doesn’t depend on the
distribution of the underlying events!

In this illustration, the number on the
top of each rolled die is an independent random event.
Independent because the result of each die roll does not depend
on the result of any previous roll, and random because, assuming
that the die is "fair", the value on the top of the
rolled die cannot be predicted in advance. The sum of their
results is the *total* number of dots on the tops of *all*
the rolled dice. The bar chart illustrates the distribution of
the sum. The distribution of each independent die roll is flat,
not bell-shaped. See for yourself. Roll one die a bunch of times
and watch the bar chart evolve. The distribution of the sum of
two independent die rolls is triangular. Try it and see. What
about five dice? What about ten?

NOTE: You must have a JAVA1.1-enabled browser to view this lab.
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Microsoft Internet Explorer 5.01 (Go to Microsoft's download page). | |

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Use your browser's BACK and FORWARD buttons to switch between this page and the lab. |