Monday, December 21, 2015

What is the Probability that X Many People will do Y?

How to Apply the Poisson Formula


Let's say there is an event you've attended for the past few years. You've had great success at this event, and you want to make sure you have enough giveaways. In the past few years you've noticed that on average 25 people visit your booth during peak time between 5 and 6 pm. These giveaways are expensive. You don't want to order too many, so you ask yourself, what is the probability of exactly 25 people showing up to the booth?

To do this you need to use what is called the Poisson Distribution. The formula looks like this:


It's fairly easy to calculate on a calculator, and you can view a great video on how to interpret this formula by clicking here.

The formula probably looks more complicated than it actually is. But in Excel or in Google Sheets, this task is very easy complete.

To do so, use =POISSON(X,MEAN,FALSE)

X = 25, which is the probability you are trying to work out
MEAN = the mean, in this case that is 25
FALSE = this is not a cumulative number - we are looking for an exact number

To solve, it is =POISSON(25,25,False), which gives us a probability of 0.08.

The chart below shows us how the probability pans out when calculated from 0 to 50 people.


Another question you might have is, "What is the probability of more than 30 people stopping by during this time frame?"

To calculate that using Excel or Sheets you use the formula:

=1-POISSON(29,25,TRUE)

This looks a bit different than the previous formula. First, there is a one in front of the formula. This is because we need to subtract the answer from the whole to calculate the answer. The other major difference is the word "TRUE" is at the end of the formula. This tells Excel or Sheets that this is "Cumulative", meaning, that we aren't looking for a specific number to calculate the probability of.

The other thing you might notice is that the X = 29. This is because we are looking for 30 and everything above it.

So when we plug this formula in, we get 0.18, meaning that there is a probability of 18% that 30 or more people will visit the booth.

The key to using this formula is to have an average number first, then you can calculate the probability of X number of people or clicks doing Y. This is a great planning tool to help you anticipate results or properly plan for results of an action taking place.




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