Assuming that 3 8 percent of the sales reps are available at any time to take a call, determine Pc during a busy period using tire Excel template on Connect, and then calculate the probability that a call during a busy period has to wait more than 30 seconds.

Call volumes to Phoenix Mutual (now Phoenix Companies Inc.), a life insurance company based in Hartford, Connecticut, had doubled and the service representatives could not answer the calls as quickly as their goal indicated they should. This occurred even though the company had installed an automatic call sequencer the year before. Customers were on hold for too long and there were too many abandoned calls. Phoenix Mutual installed an automatic call distributor and started to analyze the work of service representatives and the queuing system. The goal was to answer 85 percent of the calls in 30 seconds. There also were other tasks required of a sales rep, such as making 150 to 200 outgoing calls per day. A 1.5-month study showed that only 38 percent of an employee’s time was spent on answering calls, and another 31 percent of his or her time was classified as “available” for receiving calls. A graph of the number of incoming calls per half hour showed the peaks to be about 70 calls per half hour between 10:00 a.m.—noon and 1:00-^4:00 p.m. Within each half-hour, the number of calls each day followed a Poisson distribution. Using the service goal of answering 85 percent of incoming calls within 30 seconds and the multiple-server queuing model, Phoenix Mutual was able to determine the number of service representatives required to receive the forecasted incoming calls per half-hour of each day.