. Scheduling Patients. Prior to having an operation at a hospital, a patient is given a set of tests depending on the type of procedure (e.g., EKG, sonogram, blood work). This has to be done at least...

. Scheduling Patients. Prior to having an operation at a hospital, a patient is given a set of tests depending on the type of procedure (e.g., EKG, sonogram, blood work). This has to be done at least one week before the operation. Patients used to come in at their convenience, usually near noon or late afternoon. To avoid congestion, the hospital required that patients make an appointment for the test. The number of tests was such that patients were scheduled to arrive every u minutes. (The following model is similar to an actual study by Georgia Tech students for a hospital in Atlanta.) As an idealized model, assume that patients do indeed arrive each u minutes, and the durations of the tests are independent exponentially distributed with rate μ <>(a) Find the shortest u such that P{W˜ ≤ w} = .90 for fixed w. (b) Find the shortest u such that E[W˜ ] ≤ w and P{Q>m ˜ } ≤ .10 for fixed w and m