XL: ATP Definition: NORMSDIST

ID: Q87865

The information in this article applies to:

Microsoft Excel 98 Macintosh Edition
Microsoft Excel 97 for Windows
Microsoft Excel for Windows 95, versions 7.0, 7.0a
Microsoft Excel for Windows, versions 4.0, 5.0, 5.0c
Microsoft Excel for the Macintosh, versions 4.0, 5.0, 5.0a

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.

REFERENCES

"Handbook of Mathematical Functions," Abramowitz & Stegun, formula 26.2.17, page 932

"Microsoft Excel Function Reference," version 4.0, page 288

Additional query words: XL98 XL97 XL7 XL5 XL4 atp tool pack pak curve bell

Keywords :
Version : WINDOWS:4.0,5.0,5.0c,7.0,97; MACINTOSH:4.0,5.0,5.0a,98
Platform : MACINTOSH WINDOWS
Issue type : kbinfo