Reference no: EM132285573

The University Health System is opening a new urgent care clinic on campus. This clinic is designed to take some of the load off the hospital emergency department and other primary care providers by providing a 24 hour a day, walk-in, no appointment clinic where members of the university community can be seen for mild ailments. During the overnight hours (11 pm - 7 am), DUHS plans to staff the clinic with a single care team consisting of a nurse practitioner (NP) and an administrative assistant. The NP can only care for one patient at a time, and historical DUHS data shows that service time with the NP follows an exponential distribution with an average of 10 minutes. DUHS expects that 4 patients per hour will visit the clinic during this time, and arrivals are likely to follow a Poisson process. Answer each of the following questions for the overnight hours.

1. What is the utilization of the clinic? State your answer as a percentage with at least three decimal points, e.g., 50.000 (for 50% utilization).

2. The waiting room only has space for 3 chairs. Excess patients must wait standing up. What is the probability that any patients are standing in the waiting area? State your answer as a percentage with at least three decimal points, e.g., 50.000 (for 50% probability).

3. What is the probability that a patient has to wait more than 1 hour to complete one visit (including waiting time plus time being treated)? State your answer as a percentage with at least three decimal points, e.g., 50.000 (for 50% probability).