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The Complete Idiot's Guide to Statistics, 2nd Edition by Robert Donnelly

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Putting the Central Limit Theorem to Work

I can just sense your need right now to do something really neat with this wonderful new tool. Look no further. If we know the sample means follow the normal probability distribution and we also know the mean and standard deviation of that distribution, we can predict the likelihood that the sample means will be greater or less than certain values.
For example, let’s take our ping-pong ball experiment with n = 20. From the central limit theorem, we know the sample means follow a normal distribution with:
µ = 3.0
370
What is the probability that our next sample of 20 ping-pong balls will have a sample ...

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