The Excel NORMDIST Function


Normal Distribution
The Normal distribution is a continuous probability function that is given by the formula :

Normal Probability Density Function

where μ is the mean of the distribution, σ2 is the variance, and x is the independent variable for which you want to evaluate the function.

The Cumulative Normal Distribution function is given by the integral, from - infinity to x, of the Normal Probability Density function.

More information on the Normal Distribution is given on the Wikipedia Normal Distribution Page
NORMDIST & NORM.DIST Functions

In Excel 2010, the NORMDIST function has been replaced by the NORM.DIST function, which has improved accuracy.

Although it has been replaced, the Normdist function is still available in Excel 2010 (stored in the list of compatibility functions), to allow compatibility with earlier versions of Excel.



Basic Description

The Excel NORMDIST function calculates the Normal Probability Density Function or the Cumulative Normal Distribution Function for a supplied set of parameters.

The format of the function is :

NORMDIST( x, mean, standard_dev, cumulative )

Where the function arguments are:


x - The value at which you want to evaluate the distribution function
mean - The arithmetic mean of the distribution
standard_dev - The standard deviation of the distribution
cumulative - A logical argument which denotes the type of distribution to be used:
TRUE = Cumulative Normal Distribution Function
FALSE = Normal Probability Density Function


Normdist Function Examples

Example 1 - Normal Probability Density Function

The chart on the right shows the the Normal Probability Density Function with a mean of 40 and a standard deviation of 20.

If you want to calculate the value of this function at x = 50, this can be done using the Excel Normdist function, as follows:

=NORMDIST( 50, 40, 20, FALSE )

This gives the result 0.017603266.

Plot of Normal Probability Density Function with Mean=40 and Standard Deviation=20
Normal Probability Density Function with mean = 40 & std. dev. = 20


Example 2 - Cumulative Normal Distribution Function

The chart on the right shows the the Cumulative Normal Distribution Function with a mean of 1 and a standard deviation of 0.3.

If you want to calculate the value of this function at x = 0.8, this can be done using the Excel Normdist function, as follows:

=NORMDIST( 0.8, 1, 0.3, TRUE )

This gives the result 0.252492538.
Plot of Cumulative Normal Distribution Function with Mean=1 and Standard Deviation=0.3
Cumulative Normal Distribution Function with mean = 1 & std. dev. = 0.3

Further information and examples of the Excel Normdist function can be found on the Microsoft Office website.


Normdist Function Errors

If you get an error from the Excel Normdist function this is likely to be one of the following:

Common Errors
#NUM! - Occurs if the supplied standard_dev argument is ≤ 0
#VALUE! - Occurs if either the supplied mean or the supplied standard_dev argument is non-numeric
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