where μ is the mean of the distribution, σ^{2} 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 ∞ to x, of the Normal Probability Density function.
For further information on the Normal Distribution, see the Wikipedia Normal Distribution PageThe Excel NORM.DIST function calculates the Normal Probability Density Function or the Cumulative Normal Distribution Function for a supplied value of x, and a supplied distribution mean & standard deviation.
The Norm.Dist 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 Normdist function, which is available in earlier versions of Excel.
The syntax of the Norm.Dist function is:
Where the function arguments are listed in the table below:
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 argument which denotes the type of distribution to be used:  

Note that a mean equal to 0 and a standard deviation of 1 defines the standard normal distribution.
The above chart on the right shows the Normal Probability Density Function with a mean of 40 and a standard deviation of 20.
If you want to calculate the value of this function at x = 50, this can be done using the Excel Norm.Dist function, as follows:
This gives the result 0.017603266.
The above chart on the right shows the Cumulative Normal Distribution Function with a mean of 1 and a standard deviation of 0.3.
If you want to calculate the value of this function at x = 0.8, this can be done using the Excel Norm.Dist function, as follows:
This gives the result 0.252492538.
Further information and examples of the Excel Norm.Dist function are provided on the Microsoft Office website.
If you get an error from the Excel Norm.Dist function this is likely to be one of the following:
#NUM!    Occurs if the supplied standard_dev argument is ≤ 0. 
#VALUE!    Occurs if any of the supplied arguments are nonnumeric or nonlogical values. 