If a hospital averages three surgical cancellations per week

If a hospital averages three surgical cancellations per week, what is the probability that it will have 12 cancellations over the next 4-week period?

Solution

There are 3 per week, so there must be an average of 4*3 = 12 in the next 4 weeks.

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 =    12      
          
x = the number of successes =    12      
          
Thus, the probability is          
          
P (    12   ) =    0.114367916 [ANSWER]