Janson's Department Store in Stark, Ohio, maintains a successful catalog sales department in which a clerk takes orders by telephone. If the clerk is occupied on oneline, incoming phone calls to the catalog department are answered automatically by a recording machine and asked to wait. As soon as the clerk is free, the party who has waited the longest is transferred and serviced first. Calls come in at a rate of about 10 per hour. The clerk can take an order in an average of 3.0 minutes. Calls tend to follow a Poisson distribution, and service times tend to be negative exponential.
The cost of the clerk is 12 per hour, but because of lost goodwill and sales, Janson's loses about 30 per hour of customer time spent waiting for the clerk to take an order.
a) The average time that catalog customers must wait before their calls are transferred to the order clerk = ______ minutes (round your response to two decimal places).
