# Normal distribution is better than Poisson for large sample set?

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

1. When is it appropriate to use normal distribution when you have discrete variables ?
2. Where is Poisson distribution appropriate ?
3. What is the distribution to use to model discrete variables ?

I use Libre Office and SQL Server.

• In many real-life situations, count data is often overdispersed relative to a Poisson distribution, leading to a poor fit. This could be the case here, but I don't know since I haven't seen the data. You could try a negative binomial distribution. en.wikipedia.org/wiki/Negative_binomial_distribution – Samuel Benidt May 2 '14 at 7:51
• Also, when the expectation $\lambda$ is large, the normal becomes a good practical approximation to the Poisson distribution. You could pist your data! – kjetil b halvorsen Jan 3 '17 at 19:40