Patients arrive randomly and independently at a doctor's clinic from 8·0 A.M. at an average rate of one in Five minutes.The waiting room holds 12 persons. What is the probability that the room will be full when the doctor arrives at 9·0 A.M.?
I know how to solve some Poisson distribution based problem. But for this one I am not sure what am I missing. Can someone please help to exactly where am I wrong. According to me: Lambda = 12/hour. Number of events (desired)= 12 so Probability(12 arrivals in an hour) = e^(-12)*(12^12)/(12!). (not confident in this method though) Please help.