Poisson distribution probability
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?
Edit: I think I've put this in the wrong section. Sorry.
Re: Poisson distribution probability
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.