SOLUTION: the mean number of business failure per month in a certain town in one year is expted to be about 8.find the probability that ore than 4 businesses will fail in any given year

Question 1058341: the mean number of business failure per month in a certain town in one year is expted to be about 8.find the probability that ore than 4 businesses will fail in any given year

Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
Discrete, assume proportional to time, can be theoretically infinite (or close to it). Poisson distribution with parameter lambda=8.
The mean is 8 and the variance 8, meaning the sd is sqrt (8) or about 3.
The likelihood of more than 4 failing will be quite high. Figure out by the probability of 0,1,2,3,4 and subtract from 1.
e^(-lambda)*lambda^x/x!
p(0)=e^(-8)*8^0/0!=e^(-8)=0.0003
p(1)=e^(-8)8/1=0.0027
p(2)=e^(-8)*64/2=0.0107
p(3)=e^(-8)*512/6=0.0286
p(4)=e^(-8)*4096/24=0.0573
Those five add to 0.0137
The probability is 0.9863 it will be greater than 4.
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