Answer:
a) There is a probability of 12% that 3 hurricanes happens in any year.
b) It is expected that 5.4 years in a period of 45 years have 3 hurricanes.
c) The Poisson distribution work well in predicting this kind of events.
Step-by-step explanation:
The Poisson distribution has the following expression
[tex]P(x=k)=\frac{\lambda^ke^{-\lambda}}{k!}[/tex]
In this case we have [tex]\lambda=5.4[/tex]. The probability that, in a year, there will be 3 hurricanes is:
[tex]P(x=3)=\frac{5.4^3e^{-5.4}}{3!}=\frac{0.71}{6}=0.12[/tex]
There is a probability of 12% that 3 hurricanes happens in any year.
If we take a period of 45 years, the expected amount of years with 3 hurricanes can be estimated as:
[tex]Y=45*0.12=5.4[/tex]
It is expected that 5.4 years in a period of 45 years have 3 hurricanes.
The Poisson distribution work well in predicting this kind of events.
