Question 1127123
(a) 

What is the probability that the state will not be hit by any major hurricanes in a single& year?

Solution:

Given Poisson distribution, assuming historical trends up to the last century still apply today.

Mean number of direct hits per year, {{{lambda = 28/107}}}


{{{PMF(k,lambda)=lambda^k*((e^(-lambda))/k!)}}}


{{{k=0}}}


{{{PMF(0,lambda)=lambda^k*((e^(-lambda))/0!)}}}


={{{(28/107)^0((e^(-28/107))/0!)}}}


={{{1*((e^(-28/107))/1)}}}


={{{e^(-28/107)}}}


={{{0.7698}}}



(b) What is the probability that the state will be hit by at least one major hurricane in a single year?



{{{k>=1}}}

{{{P(k)=1-P(k=0)=1-0.7698=0.2302}}}