Poisson distribution probability

Hi,

I have the following question which I am unable to answer.

You should assume that serious earthquakes throughout the world occur at a rate of 3 per 500 days and that the number of occurrences in a given time period follows a Poisson distribution. What is the probability that exactly 4 serious earthquakes occur in a period of 200 days (3 d.p.).

The correct answer is **0.026**.

I thought it would be calculated by using the p(3 per 500) * p(4 in 200), but that does not give the correct answer.

Can anyone shed any light?

Thanks

Edit: I think I've put this in the wrong section. Sorry.

Re: Poisson distribution probability

Hey watp.

If your rate is per 500 days then you need to change the rate to per 200 days. This is achieved by multiplying the rate by 200/500 (or 0.4) and then calculating the probability that P(X = 4) under this new Poisson distribution.