# An experiment based discussion of the 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

You will choose from the pull down menu at the bottom of the page both the number of dice and the number of rolls at a time. When you "click" you will be virtually rolling your dice.

Complete 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:

1 die, 10 rolls at a time

1 die, 100 rolls at a time

1 die, 1000 rolls at a time

2 dice, 10 rolls at a time

2 dice, 100 rolls at a time

2 dice, 1000 rolls at a time

5 dice, 10 rolls at a time

5 dice, 100 rolls at a time

5 dice, 1000 rolls at a time

And because you are curious "if your computer allows" go ahead and try the experiment again with 10,000 rolls at a time

What does this experiment tell you about the Central Limit Theorem? What do you see happening as the number of die/dice being rolled changes from 1 to five? How might the number of rolls reveal an application of the Central Limit Theorem?

How is this information applicable to research in which you may be involved, including possible thesis/dissertation ideas you have?

With these thoughts in mind:

Post 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

I am not allowed to complete assignments, but I can provide you a description of what would be expected to happen with regards to the central limit theorem.

The basic idea behind the central limit theorem is that a distribution with a mean of μ and variance σ² will become normalized as the sample size is increased. This means that for a given statistic (such as height for example) ...

#### Solution Summary

An explanation of the Central Limit Theorem based on the experimental Applet found at http://www.stat.sc.edu/~west/javahtml/CLT.html. Information regarding the obtainment of a normal distribution for any randomized sample with respect to a dice rolling experiment.