$($CLO$6$ &$7)$ Arabesque Interior Design provides home and office decorating assistancis normal operation, an average of $3$ customers arrive each hour. One design consultant is available to answer customer questions and make product recommendations. The consultant averages fifteen minutes with each customer. Assume arrivals follow a Poisson distribution and service follow negative exponential distribution. $($CLO$687)$

Calculate the operating characteristics of the customer waiting line, assuming Poisson arrivals and exponential service times.

What is the probability that an arriving customer has to wait?

What percentage of the time is the consultant busy?

If a customer arrives at $10\mathrm{.}00A.M,$ at what time is he$/$she expected to leave the Arabesque office?

Service goals dictate that an arriving customer should not wait for service more than an average of five minutes. Is this goal being met? If not, what action do you recommend?