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The local hospital's emergency department has 5 trauma bays. On average, patients requiring a trauma bay arrive every 50 minutes (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 2.0 hours (with a standard deviation of 1.5 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 How many patients are treated in the trauma bays on an average 24 hour day? c The hospital updated operating procedures for staff, reducing the standard deviation of the length of stay in a trauma bay from 1.5 to 1.2 hours, but the mean remained at 2 hours. How will this training program affect the number of patients who have immediate access to a trauma bay? d New state regulations require that every emergency department be able to accommodate at least 99.5% of all patients needing a trauma bay with no 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 from the original mean of 2.0 hours.)
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