# 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:

• 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 density 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

Copy the example data in the following table, and paste it in cell A1 of a new Excel worksheet. For formulas to show results, select them, press F2, and then press Enter. If you need to, you can adjust the column widths to see all the data.

 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 0.9087888 =NORM.DIST(A2,A3,A4,FALSE) Probability mass function for the terms above 0.10934
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