For a recent period of 100 years, there were 530 Atlantic hurricanes (based on data from the University of Maryland Department of Geography and Environmental Systems). Assume that the Poisson distribution is a suitable model.

a. Find , the mean number of hurricanes per year. b. If P(x) is the probability of x Atlantic hurricanes in a randomly selected year, find P(0),P(2), and P(9). c. There were actually 2 years with no Atlantic hurricanes, 5 years with two Atlantic hurricanes, and 4 years with nine Atlantic hurricanes. How do these actual results compare to the probabilities found in part (b)? Does the Poisson distribution appear to be a good model in this case?