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 - infinity to x, of the Normal Probability Density function.More information on the Normal Distribution is given on the Wikipedia Normal Distribution Page
The Excel NORM.INV function calculates the inverse of the Cumulative Normal Distribution Function for a supplied value of x, and a supplied distribution mean & standard deviation.
The Norm.Inv 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 Norminv function that is available in earlier versions of Excel.
The format of the function is :
Where the function arguments are:
|probability||-||The value at which you want to evaluate the inverse function|
|mean||-||The arithmetic mean of the distribution|
|standard_dev||-||The standard deviation of the distribution|
Excel uses an iterative method to calculate the Norm.Inv function and seeks to find a result, x, such that:
NORM.DIST( x, mean, standard_dev, TRUE ) = probability
The chart on the right shows the the Inverse Normal Cumulative Distribution Function with a Mean of 5 and a Standard Deviation of 2.
If you want to calculate the value of this function when probability = 0.6, this can be done using the Excel Norm.Inv function, as follows:
=NORM.INV( 0.6, 5, 2 )
This gives the result 5.506694206.
Further information and examples of the Excel Norm.Inv function can be found on the Microsoft Office website.
If you get an error from your Excel Norm.Inv function this is likely to be one of the following:
Occurs if either:
- the supplied probability argument is < 0 or > 1
- the supplied standard_dev argument is ≤ 0
|#VALUE!||-||Occurs if any of the the supplied arguments are non-numeric.|