# Poisson Distribution problem in probability for engineers

1. Oct 11, 2011

### silenttube

In 2003, there were many media reports about the number of shark attacks. At the end of the year, there were a total of 30 unprovoked shark attacks. By comparison, there were 246 shark attacks over the prior ten years.

(a) Give an expression for the probability of more than 30 shark attacks occurring in a year based on the historical data (don't include data for 2003). Use a Gaussian approximation to give an approximate numerical answer.

Here I came up with the probability is 0.1171 and I am confident in this answer. B part is what I can't figure out.

(b) Suppose that the probability that there are more than 30 shark attacks in a given year is 0.1. Find the probability that there is at least one year with more than 30 shark attacks in a 10 year period.

Here I came up with 0.09 as my probability, but intuition tells me that is should probably be greater than 0.1. Any help on this problem would be appreciated.