The local hospital’s emergency department has 6 trauma bays. On average, patients requiring a trauma bay arrive every 0.4 hours (with a coefficient of variation of 1, no seasonality exists). If the hospital has an available trauma bay, it is immediately allocated to a needy patient. If there are no trauma bays available, the patient is sent to another hospital. On average, a patient’s length of stay in a trauma bay is 1.6 hours (with a standard deviation of 1.6 hours). The hospital’s emergency department operates 24 hours a day.
a. What fraction of the patients requiring trauma bays end up being sent to another hospital?
b. What is the average utilization of the trauma bays?
c. About how many patients does the hospital treat in a given day?
d. New state regulations require that every emergency department be able to accommodate at least 98% of all patients needing a trauma bay without any waiting. What is the minimum number of trauma bays necessary to meet this requirement? (Assume that the time spent in the trauma bay cannot be changed. Also, when giving the answer, please give the total number of trauma bays required, not just the number added.)