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There is the normal probability density function (pdf) which is given in the attached link. The normal probability cumulative distribution function (cdf) is used to calculate probabilities, and there is no closed form equation for this. Many statistical programs have the cdf built in. Some references are given at the end of the link to find approximate cdf. The cdf, is usually written F(x) and the pdf f(x). F(x) is the integral of f(x) from minus infinity to x.

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Q: Standard normal distribution formula
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