For the past 110 years, a certain state suffered 38 direct hits from major (cate
ID: 3062088 • Letter: F
Question
For the past 110 years, a certain state suffered 38 direct hits from major (category 3 to 5) hurricanes. Assume that this was typical and the number of hits per year follows a Poisson distribution.
(b) What is the probability that the state will be hit by at least one major hurricane in a single year?
c. What is the probability that the state will be hit by at least three major hurricanes in a single year, as happened last year?
(d) What is the probability that the certain state will be hit by at least two major hurricanes in a single year, as happened a couple of years ago?
Explanation / Answer
Given Poisson distribution, assuming historical trends up to the last century still apply today.
Mean number of direct hits per year, = 38/111
PMF(k,)=^k (e^(-)/k!
k=0
P(k=0)=^k (e^(-)/k!
=38/111^0(e^(-38/111))/0!
=1*(e^(-38/111))/1
=e^(-38/111)
=0.7101
(b) k>=1
P(k)=1-P(k=0)=1-0.7101=0.2899
(c) P(k>=3)=1-(P(k=0)+P(k=1)+P(k=2))
=1-(0.7101+0.2430+0.0416)
=1-0.9947
=0.0053
(d) P(k>=2)=1-(P(k=0)+P(k=1))
=1-(0.7101+0.2430)
=1-0.9531
=0.0469