Normal distribution formula

Few statistics textbooks are likely to tell you what the formula for the normal distribution is. Many will still give you tables of values derived from the formula, and it is built into most statistics software. (For example, in Microsoft Excel, you can use the NORMDIST function.) So you do not need to know it.

For the curious, here it is:

Here, x is the distance from the mean in standard deviations and e is Euler's constant (2.71828...).

Source:

In practice, the ratio between the x and y scales varies. So the formula can be simplified to
y = k e -x2/2
 
where k is constant for a given set of data.


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Last updated November 12, 1999.
This page maintained by Prof. Tim Craven
E-mail (text/plain only): t.craven@uwo.ca
Faculty of Information and Media Studies
University of Western Ontario,
London, Ontario
Canada, N6A 5B7