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 -∞ to x, of the Normal Probability Density function.

For more information on the Normal Distribution, see 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In Excel 2010, the NORMDIST function has been replaced by the NORM.DIST function, which has improved accuracy.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 syntax 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

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

The chart on the rightabove chart shows 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.


Example 2 - Cumulative Normal Distribution Function

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

The chart on the rightabove chart shows 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.


Further details and examples of the Excel Normdist function are provided 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 any of the supplied arguments are non-numeric or non-logical values.