Instead of rolling a die 100 times, use a calculator (TI83/84) or STATDISK to simulate 100 rolls of a die. Select one of the following random generators that produces the whole numbers 1, 2, 3, 4, 5, 6 randomly.

Without actually generating a histogram of the original 5000 rolls, what would you expect the shape of the 5000 simulated roll of a die to be? How does that compare to the histogram that you just created of the 50 sample means?

Explain, in your own words, how this demonstrates the Central Limit Theorem. Be specific and clear.

How does the mean of the 100 sample means compare to the mean of many rolls of a fair die?

How does the standard deviation of the sample means compare to the standard deviation of outcomes when a single die is rolled a large number of times.

How do these results demonstrate the Central Limit Theorem? Explain in your own words using you own results. Be specific and clear.