#### ccurtis

##### Well-Known Member

Just for fun I have collected data, 40 points so far, of the daily time of arrival of snail mail to my house. I applied normal distribution stats to the data to get an objective view of the probability of receiving mail within certain time intervals. But, there is an issue. The data distribution does not appear to be bell shaped (normal). The left tail of the curve is short and there is a long tail on the right side. There is a hard limit to how early the mail arrives, yet, the mail arrives, albeit infrequently, well after dark. The 3 sigma time interval gives an early time of arrival that is apparently impossible while giving a late time interval that is reasonable.

Question 1: Does this mean that application normal distribution is a flawed model?

Question 2: Is there a better model for this situation? I read about a Poisson distribution model, but it talks about rates of events so I doubt applicability, although the curve shape looks like a fit. Only one event occurs per day, never more than one event per unit time.