A network administrator is installing a videoconferencing module in a local area network (LAN) computer system. Of interest is the capacity of the LAN to handle users who attempt to call in for videoconferencing during peak hours. Calls are blocked if the user finds that all LAN lines are "busy." The capacity is directly related to the rate at which calls are blocked. Let x equal the number of calls blocked during the peak hour (busy) videoconferencing call time. The network administrator believes that x has a Poisson distribution with mean =5.

a) Find the probability that fewer than 3 calls are blocked during the peak hour.

b) Find the expected value mean E(x) and interpret its value.

c) Is it likely that no calls will be blocked during the peak hour? What is the probability of no calls will be blocked?