Microsoft KB Archive/214111

= XL2000: ATP Definition: NORMSDIST =

Article ID: 214111

Article Last Modified on 10/8/2003

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APPLIES TO


 * Microsoft Excel 2000 Standard Edition

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This article was previously published under Q214111





SUMMARY
Microsoft Excel 2000 provides a set of special analysis tools called the Analysis ToolPak. This article is part of a series of articles that provide information about the underlying formulas used in the Analysis ToolPak.

This article covers the NORMSDIST(z) function.



MORE INFORMATION
The NORMSDIST function returns the result of the standard normal cumulative distribution function for a particular value of the random variable X. The Excel function adheres to the following mathematical approximation, P(x), of the following standard normal cumulative distribution function (CDF)   P(x) = 1 -Z(x)*(b1*t+b2*t^2+b3t^3+b4t^4+b5t^5)+error(x), where

Z(x) = (1/(sqrt(2*pi))*exp(-x^2/2)) t = 1/(1+px) p = 0.2316419 b1 = 0.319381530 b2 = -0.356563782 b3 = 1.781477937 b4 = -1.821255978 b5 = 1.330274429 with the following parameters:

abs(error(x))<7.5 * 10^-8

The NORMSDIST function returns the result of the standard normal CDF for a standard normal random variable Z with a mean of 0 (zero) and a standard deviation of 1. The CDF is found by taking the integral of the following standard normal probability density function

Z(x) = (1/(sqrt(2*pi))*exp(-x^2/2))

from negative infinity to the value (z) of the random variable in question. The result of the integral gives the probability that Z will occur between the values of negative infinity and z.

