Question

Off the coast of a highly populated island, there have been a number of fatal sharks over the years. It was found the the average number of fatal shark attacks per year is 11.1.

Round all probabilities to four decimal places.

(a) Find the probability there are exactly 9 fatal shark attacks off the coast of this island in any given year.

(b) Find the probability that there at least 9 fatal shark attacks off the coast of this island in any given year.

(c) It would be unusual to have more than fatal shark attacks off the coast of this island in any given year.

Answer 1

Solution:

Given that (Average number of fatal shark attacks per year) = 11.1

Using Poisson distribution formula, we get

P (X = x) =

a. P (X = 9) =

P (X = 9) = 0.1065

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b. P (X 9) = 1 - P (X < 9)

= 1 - [P (X = 0) + P (X = 1) + P (X = 2) + P (X = 3) + P (X = 4) + P (X = 5) + P (X = 6) + P (X = 7) + P (X = 8)]

=

= 1 - (0.0000 + 0.0002 + 0.0009 + 0.0034 + 0.0096 + 0.0212 + 0.0393 + 0.0623 + 0.0864]

= 1 - 0.2232

= 0.7768

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c. P (X > 9) = 1 - P (X 9)

= 1 - (0.2232 + 0.1065)

= 0.6703

Since the probability is large, it would be not unusual.