Question: Question regarding utilization, probability, relating to Operations: Assume a hospital provides 24hr service, walk-in, no appointment necessary operation. From 11pm - 7am they plan to

Question regarding utilization, probability, relating to Operations:

Assume a hospital provides 24hr service, walk-in, no appointment necessary operation. From 11pm - 7am they plan to staff the hospital with 1 care team consisting of a nurse and admin assistant. The nurse can only care for 1 patient at a time, and historical data shows service time with the nurse follows exponential distribution w/ an average of 10min. The hospital expects that 4 patients/hr. will visit the clinic during this time. Arrivals follow a Poisson process. Answer the follow questions for overnight hours rounded to three decimals: 1. What is the utilization rate of the hospital? 2. The waiting room has space for 3 chairs. Excess patients wait by standing up. Calculate the probability that patients are standing in the waiting area. 3. Calculate the probability percentage that a patient must wait >1hr to complete a visit (do include the waiting time as well as time being treated)

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