One of the earliest applications of the Poisson distribution was in analyzing incoming calls to a telephone switchboard. Analysts generally believe that random phone calls are Poisson distributed. Suppose phone calls to a switchboard arrive at an average rate of 2.4 calls per minute.
a)If an operator can handle at most five calls per minute, what is the probability that the operator will be unable to handle the calls in any 1-minute period?
b)What is the probability that one or fewer calls will arrive in a 15-second interval?