Applies ToExcel for Microsoft 365 Excel for Microsoft 365 for Mac Excel for the web Excel 2024 Excel 2024 for Mac Excel 2021 Excel 2021 for Mac Excel 2019 Excel 2016

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:

    Equation

  • 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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