At a local crisis center, three volunteers answer the phones to help solve residents' problems. Calls arrive randomly, at an average rate of 20 per eight hour day (crisis center operates for 8 hours only). The amount of time that a volunteer spends with a caller is exponentially distributed with an average of 40 minutes. If all the volunteers are busy, the callers are put on hold and they are assigned in the order of their arrival. a) Determine the fraction of time each volunteer is busy. b) On the average, how long is a caller put on hold? c) On the average, how many callers are on hold? d) How much time on the average, does a caller spend on the phone? e) What is the average number of callers tied up to the phone? f) Determine the probability that all volunteers are idle. g) Find the probability that all the volunteers are busy yet no caller is on hold.