The number and frequency of Atlantic hurricanes annually from 1940 through 2007 is shown here:

a. Find the probabilities of 0-8 hurricanes each season using these data

b. Assuming a Poisson distribution and using the mean number of hurricanes per season from the empirical data, compute the probabilities of experiencing 0-8 hurricanes in a season.

Compare these to your answer to part (a).

How good does a Poisson distribution model this phenomenon?

Number Frequency
0 5
1 16
2 19
3 13
4 3
5 5
6 4
7 2
8 1
Total 68

The probability table is shown below.

A Poisson distribution can be used to approximate the model of the number of hurricanes each season.

Step-by-step explanation:

(a)

The formula to compute the probability of an event E is:

Use this formula to compute the probabilities of 0 - 8 hurricanes each season.

The table for the probabilities is shown below.

(b)

Compute the mean number of hurricanes per season as follows:

If the variable X follows a Poisson distribution with parameter λ = 7.56 then the probability function is:

Compute the probability of X = 0 as follows:

Compute the probability of X = 1 as follows:

Compute the probabilities for the rest of the values of X in the similar way.

The probabilities are shown in the table.

On comparing the two probability tables, it can be seen that the Poisson distribution can be used to approximate the distribution of the number of hurricanes each season. This is because for every value of X the Poisson probability is approximately equal to the empirical probability.

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