A new phone answering system for a company is capable of handling sevenseven calls every 10 minutes. Prior to installing the new
system, company analysts determined that the incoming calls to the system are Poisson distributed with a mean equal to fourfour every 10 minutes. If this incoming call distribution is what the analysts think it is, what is the probability that in a 10-minute period more calls will arrive than the system can handle?
P = probability of more calls than system can handle = 1 – (probability of 0 calls + probability of 1 call + probability of 2 calls + probability of 3 calls + probability of 4 calls + probability of 5 calls)