anson's Department Store in$$ Stark, Ohio, maintains a successful catalog sales department in which a clerk takes orders by telephone. If the clerk is occupied on one$$ line, incoming phone calls to the catalog department are answered automatically by a recording machine and asked to wait. As soon as the clerk is$$ free, the party who has waited the longest is transferred and serviced first. Calls come in at a rate of about $11$ per hour. The clerk can take an order in an average of $4\mathrm{.}0$ minutes. Calls tend to follow a Poisson$$ distribution, and service times tend to be negative exponential.

The cost of the clerk is $$$$8$ per$$ hour, but because of lost goodwill and$$ sales, Janson's loses about $$$$27$ per hour of customer time spent waiting for the clerk to take an order.

Part $2$

$$a$)$ The average time that catalog customers must wait before their calls are transferred to the order clerk$=$

enter your response here

minutes $($round your response to two decimal$$ places$).$