I discuss the central limit theorem, a very important concept in the world of statistics. I illustrate the concept by sampling from two different distributions, and for both distributions plot the sampling distribution of the sample mean for various sample sizes. I also discuss why the central limit theorem is important in statistics, and work through a probability calculation. (For the most part this is a nontechnical treatment, and simply illustrates the important implications of the central limit theorem.)

For those using R, here is the R code to find the probability for the example in this video:

Finding the (approximate) probability that the mean salary of 100 randomly selected employees exceeds $66,000:
1pnorm(66000,62000,32000/sqrt(100))
[1] 0.1056498

Or, standardizing:
1pnorm((6600062000)/(32000/sqrt(100)))
[1] 0.1056498
1pnorm(1.25)
[1] 0.1056498