The Excel NORM.DIST Function

Related Functions:
NORM.INV
NORM.S.DIST
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 further information on the Normal Distribution, see the Wikipedia Normal Distribution Page

Basic Description

The Excel NORM.DIST function calculates the Normal Probability Density Function or the Cumulative Normal Distribution Function for a supplied value of x, and a supplied distribution mean & standard deviation.

The Norm.Dist function is new in Excel 2010 and so is not available in earlier versions of Excel. However, the function is simply a new version of the Normdist function, which is available in earlier versions of Excel.

The syntax of the Norm.Dist function is:

NORM.DIST( x, mean, standard_dev, cumulative )

Where the function arguments are listed in the table below:

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

Note that a mean equal to 0 and a standard deviation of 1 defines the standard normal distribution.


Norm.Dist 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 above chart on the right 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 Norm.Dist function, as follows:

=NORM.DIST( 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 above chart on the right 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 Norm.Dist function, as follows:

=NORM.DIST( 0.8, 1, 0.3, TRUE )

This gives the result 0.252492538.


Further information and examples of the Excel Norm.Dist function are provided on the Microsoft Office website.


Norm.Dist Function Errors

If you get an error from the Excel Norm.Dist 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.