XL2000: ATP Definition: NORMSDIST (214111)

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.

REFERENCES

For more information about the algebraic representation of the Normsdist function, click Microsoft Help on the Help menu, type normsdist in the Office Assistant or the Answer Wizard, and then click Search to view the topic.

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