For a recent period of 100 years there were 530 Atlantic hur

.For a recent period of 100 years, there were 530 Atlantic hurricanes (based on data from the University of Maryland Department of Geography and Environmental Systems). Assume that the Poisson distribution is a suitable model.

a. Find µ, the mean number of hurricanes per year.

b. If P(x) is the probability of x Atlantic hurricanes in a randomly selected year, find P(0), P(2), and P(9).

Solution

A)

There are u = 530/100 = 5.3 hurricanes per year.

b)

Note that the probability of x successes out of n trials is          
          
P(x) = u^x e^(-u) / x!          
          
where          
          
u = the mean number of successes =    5.3      
          
x = the number of successes =    0      
          
Thus, the probability is          
          
P (    0   ) =    0.004991594 [ANSWER]

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Note that the probability of x successes out of n trials is          
          
P(x) = u^x e^(-u) / x!          
          
where          
          
u = the mean number of successes =    5.3      
          
x = the number of successes =    2      
          
Thus, the probability is          
          
P (    2   ) =    0.070106936 [ANSWER]

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Note that the probability of x successes out of n trials is          
          
P(x) = u^x e^(-u) / x!          
          
where          
          
u = the mean number of successes =    5.3      
          
x = the number of successes =    9      
          
Thus, the probability is          
          
P (    9   ) =    0.045389881 [ANSWER]