# NORM.DIST function

Returns the normal distribution for the specified mean and standard deviation. This function has a very wide range of applications in statistics, including hypothesis testing.

## Syntax

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

The NORM.DIST function syntax has the following arguments (argument: A value that provides information to an action, an event, a method, a property, a function, or a procedure.):

• X     Required. The value for which you want the distribution.
• Mean     Required. The arithmetic mean of the distribution.
• Standard_dev     Required. The standard deviation of the distribution.
• Cumulative     Required. A logical value that determines the form of the function. If cumulative is TRUE, NORM.DIST returns the cumulative distribution function; if FALSE, it returns the probability mass function.

## Remarks

• If mean or standard_dev is nonnumeric, NORM.DIST returns the #VALUE! error value.
• If standard_dev ≤ 0, NORM.DIST returns the #NUM! error value.
• If mean = 0, standard_dev = 1, and cumulative = TRUE, NORM.DIST returns the standard normal distribution, NORM.S.DIST.
• The equation for the normal density function (cumulative = FALSE) is:

• When cumulative = TRUE, the formula is the integral from negative infinity to x of the given formula.

## Example

The example may be easier to understand if you copy it to a blank worksheet.

1. Select the example in this article. If you are copying the example in Excel Web App, copy and paste one cell at a time.Important Do not select the row or column headers.

Selecting an example from Help

1. Press CTRL+C.
2. Create a blank workbook or worksheet.
3. In the worksheet, select cell A1, and press CTRL+V. If you are working in Excel Web App, repeat copying and pasting for each cell in the example.

Important For the example to work properly, you must paste it into cell A1 of the worksheet.

1. To switch between viewing the results and viewing the formulas that return the results, press CTRL+` (grave accent), or on the Formulas tab, in the Formula Auditing group, click the Show Formulas button.

After you copy the example to a blank worksheet, you can adapt it to suit your needs.

A B
Data Description
42 Value for which you want the distribution
40 Arithmetic mean of the distribution
1.5 Standard deviation of the distribution
Formula Description (Result)
=NORM.DIST(A2,A3,A4,TRUE) Cumulative distribution function for the terms above (0.908789)
=NORM.DIST(A2,A3,A4,FALSE) Probability mass function for the terms above (0.10934005)

Applies to:
Excel 2010, Excel Web App, SharePoint Online for enterprises, SharePoint Online for professionals and small businesses