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February 29th, 2016, 08:27 AM   #1
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Normal distribution: a probability distribution?

Hi!

My professor said that we were going to look at different probability distributions and that the normal distribution is one of them. But in our textbook it says that the probability distribution will resemble the normal distribution graph when the sample is large enough. If this is right, it does not make much sense to me that the normal distribution IS a probability distribution. Does anyone know what is right? If so, may you explain?
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February 29th, 2016, 09:43 AM   #2
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The normal distribution is a probability distribution because it describes the probability that a random variable X will fall within some range. For example, you can evaluate P(Z > 0) to be 0.5, P(-1 < Z < 1) to be 0.68, and so on.

You seem to be confused by the Central Limit Theorem, which purports that as the number of samples you take from any underlying distribution tends to infinity, the sample mean will tend to the normal distribution. That's true, but it doesn't mean that normal distributions only exist under sampling. It also appears everywhere from test scores to children's heights.

I suggest you study and understand the normal distribution as a probability distribution first, then look at the Central Limit Theorem when you deal with statistical inference.
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February 29th, 2016, 12:49 PM   #3
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Thank you so much for your answer! I'm so grateful. I think I finally got the hang of it, or at least a better understanding.
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February 29th, 2016, 05:35 PM   #4
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What your professor is saying is the 'law of large numbers' that essentially says that all probability distributions approach the normal probability distribution for sufficiently large number of trials. But that does not mean that it is not itself a probability distribution!
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