The central limit theorem explains why it is so critical to understand the normal distribution.
Suppose we have a population set of data. It has a mean, µ, and a standard deviation, σ.  If we created a histogram for this data, it could be uniform, or skewed or bimodal, or whatever.
The central limit theorem says that if we determine the mean of many samples (n > 30 is best) and make a new histogram, it will be normal!  The new mean of these samples is the same as the original mean of the population and the new standard deviation of these samples is the standard deviation of the population divided by the square root of n.

Go to this website.    http://onlinestatbook.com/stat_sim/sampling_dist/

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This allows us to run virtual sampling distributions. The top histogram is our population. If gives the options of uniform, normal, skew, or custom.
Initial Post:

Choose CUSTOM and use the mouse to trace your own distribution (just don’t make it a normal distribution). The whole point of this is to see that even if the population is not normal, the sampling distribution will in fact be normal (if N > 30 or even if N > 25…) .
On the third graph down, select N=25. This will select 25 items from the population, then plot the sample mean on the graph.
Hit ANIMATE on the second graph once to see this happen once. Then hit “5” to see it done 5 times, then hit “10,000” to see the process repeated that many times. Now you should hopefully see that the sampling distribution graph (third one down) is now approximately normal!
At this point, take a SCREENSHOT of the top three graphs, including the statistics to the left (see my example post as an example). If you don’t know how to take a screenshot, use Google to learn how with either a Mac or Windows.
You will POST YOUR SCREENSHOT into the discussion board. You’ll need to resize it to make it smaller, but still legible.

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