# When to use Poisson distribution?

I'm slightly confused with when I should use a Poisson distribution.

If I have a case where:

• I have the sample mean of the number of events happening in a particular day (say it is 1.27).
• Five days are randomly selected from a sample.

Can I use the Poisson process to find the probability that the sample mean now is more than 0.3?

• I'm not completely sure I understand your description, but it sounds like you're trying to construct some kind of interval for a Poisson mean for some unobserved time period based on a sample for some other time period. Is that correct? – Glen_b -Reinstate Monica Feb 20 '14 at 13:53
• Thanks for the speedy reverts Glen. I'm not quite sure if Poisson is the game here. What i have on hand is a probability distribution of the number of events happening on a particular day - from which I've worked out the mean. What i want to find out is the probability that this mean is going to be more than 0.3 if 4 days are randomly selected from a sample. Is the sample size important? – user1275515 Feb 20 '14 at 14:01
• Oh, I think I see. You've been given some probability distribution for a random variable representing the number of events per day. You computed the mean of that distribution (a population mean). Then you start talking about a sample mean over several days of observations. Is that it? (There are several strange things about your wording that make it especially confusing.) – Glen_b -Reinstate Monica Feb 20 '14 at 14:30
• Spot on Glen! You're really brilliant. Yeps. Thats what Im trying to self learn and solve – user1275515 Feb 20 '14 at 14:35
• I will say that there's no hint in the little information you give that the Poisson comes into this at all. A little more detail might clarify that. – Glen_b -Reinstate Monica Feb 20 '14 at 22:33