Microsoft KB Archive/87865

= ATP Definition: NORMSDIST =

Article ID: 87865

Article Last Modified on 11/16/2006

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APPLIES TO


 * Microsoft Excel 97 Standard Edition
 * Microsoft Excel 95 Standard Edition
 * Microsoft Excel 5.0 Standard Edition
 * Microsoft Excel 98 for Macintosh

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This article was previously published under Q87865





SUMMARY
The versions of Microsoft Excel listed at the beginning of this article provide 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 following function:

  NORMSDIST(z)



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 Microsoft Excel function adheres to the following mathematical approximation, P(x), of the standard normal 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 these parameters, abs(error(x))<7.5 * 10^-8.

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

