A regional director responsible for business development in

A regional director responsible for business development in the state of Pennsylvania is concerned about the number of small business failures. If the mean number of small business failures per month is 11.2, what is the probability that exactly four small businesses will fail during a given month (to 4 decimals)? Assume that the probability of a failure is the same for any two months and that the occurrence or nonoccurrence of a failure in any month is independent of failures in any other month.

Solution

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 =    10      
          
x = the number of successes =    4      
          
Thus, the probability is          
          
P (    4   ) =    0.018916637 [ANSWER]