POS 1:

Hello Class,

Sampling with a Pair of Dice.

The results from the 10 rolls of dice average to 7.6

And the results from the 20 rolls of dice average to 7.1

In this example of random sampling, we see that the Central Limit Theorem holds true for the sampling distribution of the sample mean can be approximated by a normal distribution as the sample size becomes large.

POST 2:

I found it interesting that the central limit theorum is good, it is not infallable. When I did the first run through of my numbers, I got the following results:

 Roll # Die 1 Die 2 Sum 1 3 6 9 2 3 2 5 3 2 4 6 4 5 2 7 5 1 2 3 6 4 1 5 7 4 3 7 8 4 5 9 9 4 5 9 10 2 3 5 SUM 65 Average 6.5 Roll # Die 1 Die 2 Sum 1 6 6 12 2 4 2 6 3 6 4 10 4 2 2 4 5 2 4 6 6 4 2 6 7 3 1 4 8 2 4 6 9 3 4 7 10 3 2 5 11 1 6 7 12 5 5 10 13 6 3 9 14 6 1 7 15 1 5 6 16 4 6 10 17 6 3 9 18 2 6 8 19 1 4 5 20 2 3 5 SUM 142 Average 7.1

This shows that the larger the sample, the closer to the mean of 7 (which is the average of two dice being added together, where you can roll from a 2 to a 12), but it is not perfect. Just for kicks, I tried running it a few more times, only to discover that on two of 5 sets, my 10 roll average was closer to the mean than the 20 rolls.