The local hospital’s emergency department has 6 trauma bays. On average, patients requiring a trauma bay arrive every 30 minutes (with a coefficient of variation of 1). 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 1.5 hours (with a standard deviation of 1.5 hours). The hospital’s emergency department operates 24 hours a day.
1. What percentage of the patients requiring trauma bays end up being sent to another hospital?
2. New state regulations require that every emergency department be able to accommodate at least 97% of all patients needing a trauma bay without any waiting. What is the minimum number of trauma bays necessary to meet this requirement?