# Central Limit Theorem

? Visit the following Web site Central Limit Theorem Applet and read what is posted: http://www.stat.sc.edu/~west/javahtml/CLT.html

? From the pull down menu at the bottom of the page, choose 5 for number of dice. For the number of rolls at a time from that menu, again choose 5.

? Click to roll your virtual dice. Keep track of how many clicks (rolls) it takes to achieve a "normal curve."

? Repeat the experiment using the following conditions. Note: You may need to click your Web browser's Refresh or Reload button to reset the experiment. Each time you repeat the experiment, keep track of how many clicks (rolls) it takes to produce a normal distribution:

? 5 dice, 10 rolls at a time

? 5 dice, 100 rolls at a time

? And because you are curious?if your computer allows?go ahead and try the experiment again with 5 dice, 1,000 rolls at a time; and 5 dice, 10,000 rolls at a time.

? What does this experiment tell you about the Central Limit Theorem?

? How is this information applicable to research

With these thoughts in mind:

Summary of task: create a report of how many clicks (rolls) it took under each condition to produce a normal distribution, a brief explanation of what conducting these experiments tells you about the Central Limit Theorem, and how this information may apply to research in which you may be involved.

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#### Solution Preview

? 5 dice, 10 rolls at a time

It took me about 45 times to get it looking like a decent Normal distribution. If I were a bit more lenient I could have called it "normal" around the 25th roll, but one column tended to stick out too far making it a bit left-skewed.

? 5 dice, 100 rolls at a time

It only took 4 rolls this time.

? And because you are curious?if your computer allows?go ahead and try the experiment again with 5 dice, 1,000 ...

#### Solution Summary

The Central Limit Theorem is investigated using the rolling dice experiment. The solution is detailed and has a '5/5' rating.