The number and frequency of Atlantic hurricanes annually from 1940 through 2015 is shown here. This means, for instance, that no hurricanes occurred during 5 of these years, only one hurricane occurred in 16 of these years, and so on.

a. Find the probabilities of 0–12 hurricanes each season using these data. 

b. Find the mean number of hurricanes. 

c. Assuming a Poisson distribution and using the mean number of hurricanes per season from part b, compute the probabilities of experiencing 0–12 hurricanes in a season. Compare these to your answer to part a. How accurately does a Poisson distribution model this phenomenon? Construct a chart to visualize these results

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Number 0 1 2 3 4 567 8 10 12 Frequency 5 16 20 14 4 5 5 3 2 1 1