The number and frequency of a certain ocean's hurricanes annually from 1935 through 2010 is shown below. This means, for instance, that no hurricanes occurred during 5 of these years, only one hurricane occurred in 13 of these years, and so on. Complete parts a through c below.

Number	0	1	2	3	4	5	6	7	8	10	12
Frequency	5	13	20	17	3	5	4	4	2	1	1

1. Find the probabilities of 0-12 hurricanes each season using these data.

Number	0	1	2	3	4	5	6	7	8	10	12
Frequency	5	13	20	17	3	5	4	4	2	1	1
Probability

1. Find the mean number of hurricanes.

1. Assuming a Poisson distribution and using the mean number of hurricanes per season from part b, compute the probabilities of experience 0-12 hurricanes in a season.

Number	0	1	2	3	4	5	6	7	8	10	12
Frequency	5	13	20	17	3	5	4	4	2	1	1
Poisson Probability

Compare the probabilities assuming a Poisson distribution to your answers in part a. Divide each Poisson probability by its respective probability to get a measure of their relative ratios.

Number	0	1	2	3	4	5	6	7	8	10	12
Frequency	5	13	20	17	3	5	4	4	2	1	1
Ratio

Construct a chart to visualize these results.

How accurately does a Poisson distribution model this phenomenon? (mult choice)

1. The Poisson distribution is a very inaccurate model of this phenomenon.
2. The Poisson distribution is a very accurate model of this phenomenon.
3. The Poisson distribution overestimates for the extreme numbers and underestimates for the central numbers.
4. The Poisson distribution overestimates for the central numbers and underestimates for the extreme numbers.