XL: ATP Definition: NORMSDIST

• 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

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