The 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.

  • This function was introduced in Excel 2010 and so is not available in earlier versions.
  • The NORM.DIST function replaces the NORMDIST function included in earlier versions of Excel.

Syntax

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

Arguments

Argument Description
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 value that determines the form of the function

  TRUE returns the cumulative distribution function
  FALSE returns the probability mass function

Examples

  A B C D
1 Data Description    
2 20 Value for which you want the distribution    
3 15 Arithmetic mean of the distribution    
4 1.5 Standard deviation of the distribution    
5        
6 Formula Result Notes
7 =NORM.DIST(A2,A3,A4,TRUE) 0.999571 Cumulative distribution function for the terms above
8 =NORM.DIST(A2,A3,A4,FALSE) 0.001028 Probability mass function for the terms above

Common Function Error(s)

Problem What went wrong
#VALUE! Occurs if any of the supplied arguments are non-numeric or non-logical values
#NUM! Occurs if the supplied standard_dev argument is ≤ 0

The equation for the normal density function (cumulative = FALSE) is:    

    \[    f(x \mid \mu,\sigma) = \frac 1{\sqrt{2\pi} \sigma} e^{- \frac {(x-\mu)^2}{2\sigma^2}    \]

where \mu is the mean of the distribution, \sigma^2 is the variance, and x is the independent variable for which you want to evaluate the function.

See Wikipedia for more information on normal distribution.