Problem

Visit the web site of the Journal of Statistics Education. This site provides an interactive example demonstrating the central limit theorem using simulated dice-rolling experiment. For your first simulation, set the number of dice to 1 and the number of rolls to 10. Repeatedly and rapidly, press the "roll the dice" button. Each time you press it the die will be rolled 10 more times and the results will be added to the previous roll.

Look for convergence. That means that as you keep pushing the "roll the dice" button, the histogram will approach a particular shape.

Now try the same thing with number of dice set to 2. Now try it with 3, then 4, then 5.

To what shape does the histogram converge when you roll 1 die at a time? What happens when you roll a pair of dice? When you roll 3 dice? 4 dice? 5 dice?

Each time you change the number of dice, the simulator will start all over. Try it several times. You might also want to try changing the number of rolls. If you set it to 1, each time you push the button you will get one roll of however many dice you chose. If you set it to 100, each time you push the button it will be as if you set it to 1 and pressed the button 100 times.

Discuss a normal distribution and what it implies. Are there other distribution patterns?