The Poisson distribution is a discrete probability function that can be used to find the probability of a number of events occurring in a specified time period.
The Poisson probability mass function shows the probability of exactly x occurrences, and is given by :where λ is the expected number of occurrences within the specified time period.
The cumulative distribution function shows the probability of at most x occurrences, and is given by :More information on the Poisson Distribution is given on the Wikipedia Poisson Distribution PageThe Excel POISSON.DIST function calculates the Poisson Probability Mass Function or the Cumulative Poisson Probability Function for a supplied set of parameters.
The function is new to Excel 2010 and so is not available in earlier versions of Excel. However the Poisson.Dist function is simply a new version of the Poisson function, which is available in earlier versions of Excel.
The format of the function is :
Where the function arguments are listed in the following table :
x    The number of events that we want the probability for (must be ≥ 0) x should be an integer; If supplied as a decimal, Excel will truncated this to an integer  
mean    The expected number of events (must be ≥ 0)  
cumulative    A logical argument that specifies the type of distribution to be calculated. This can be either:

The above chart on the right shows the Poisson Probability Mass Function with an expected value (mean) equal to 25.
If you want to calculate the value of this function at x = 40, this can be done using the Excel Poisson.Dist function, as follows:
This gives the result 0.051917469.
The above chart on the right shows the Cumulative Poisson Probability Function with an expected value (mean) equal to 40.
If you want to calculate the value of this function at x = 25, this can be done using the Excel Poisson.Dist function, as follows:
This gives the result 0.242414198.
Further information and examples of the Excel Poisson.Dist function can be found on the Microsoft Office website.
If you get an error from the Excel Poisson.Dist function this is likely to be one of the following :
#NUM!    Occurs if either of the supplied x or mean arguments are < 0 
#VALUE!    Occurs if either of the supplied x or mean arguments are nonnumeric 