Gaussian Probability Calculator

x =

Mean =

Standard Deviation =

Gaussian Approximation =

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Calculates an excellent approximation (within 0.27%) for the probability of a random variable X that has a Gaussian Probability Density Function.

This template will accept and invert values of X less than the mean, or X less than zero in the case of standardized values.

It will also standardize the Random Variable if Ax and Px are given.

For pre-standardized values of X use:

Ax=0

Px=1

- Fx: Gaussian Approximation

- x: Variable

- Ax: Mean

- Px: Standard Deviation

StandardX = (x-Ax)/Px

Fx =1 - ( 1 / (.661 * StandardX + .339 * sqrt(StandardX² + 5.51)) * exp(-StandardX² / 2)/sqrt(2 * pi))

Gaussian Approximation

Mean

Standard Deviation

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