Question

Assume that the Poisson distribution applies and that the mean number of hurricanes in a certain area is 7.67.6 per year.

a. Find the probability​ that, in a​ year, there will be 66 hurricanes.

b. In a 3535​-year period, how many years are expected to have 66 hurricanes?

c. How does the result from part​ (b) compare to a recent period of 3535 years in which 44 years had 66 hurricanes? Does the Poisson distribution work well​ here?

Answer 1

a)

P(X=6)=

{e-7.6*7.66/6!}=

0.133940 (please take care of decimals as required in question)

b)

expected number =np= 35*0.13394 =4.6879

(please take care of decimals as required in question)

c)

the result is close to actual value, poisson distribution works well here