I'm at a beginner level, so please bear with me.
This is a call center use case. For every week, certain number of calls are received. The average is about 20. This seemed like a Poisson distribution to me (rate per interval). I took about 100 data points. I tried to answer the question "what is the probability of receiving more than 5,10,20,30 etc. calls per week". I computed the corresponding Poisson results. I created another column and answered the same question using Normal distribution. I then generated the probability by directly querying from the database (ie # of weeks where there were more than x calls/total number of weeks). I found something interesting, the actual data followed Normal distribution and not Poisson distribution. Why is that ? I assumed that "number of calls" is discrete & so it should be Poisson.
The question I'm getting at is
- When is it appropriate to use normal distribution when you have discrete variables ?
- Where is Poisson distribution appropriate ?
- What is the distribution to use to model discrete variables ?
I use Libre Office and SQL Server.