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7Clinical Trials Calls:Researchers at the medical school conducting clinical trials areenrolling subjects.They air radio ads and receive an average of 12 calls per hour frominterested patients.Times between call arrivals are exponentially distributed.A nurseanswers the calls and screens potential subjects.Call time durations are exponentiallydistributed and last an average of 4 minutes. Three out of every four callers are rejectedafter the first screen. All others are transferred to a research assistant for a second screen,involving a longer phone interview that lasts 15 minutes on average with a standard devi-ation of 3 minutes. If the research assistant is busy when callers are transferred, they areput on hold and their calls are taken in the order they were received.a. How long do callers spend on average, from the time they call until they are rejectedor transferred?b. When callers are transferred, how long on average do they wait on-hold until theystart speaking to the research assistant?c. On average, what is the total number of callers on hold across both screening sages?
8Flu Vaccinations:A local organization has set up a temporary free flu vaccination centerfor senior citizens. The process consists of three steps: Arriving patients wait in a queuean average of 3 minutes and visit the first desk, staffed by a retired physician in whichpatients are greeted and given a questionnaire to fill up. That physician spends an averageof 2 minutes with each patient. Patients are then directed to a second line, where theywait an average of 5 minutes (during which they fill out their questionnaires), after whichthey talk to one of two medical students who check their answers and spend an averageof 6 minutes with each patient. Finally, patients are sent to the last line, where they waitan average of 4 minutes and are then seen by one of five nurses, who administer the shots.Each patient spends an average of 10 minutes with a nurse.a. How long does an average patient spend in the three step process from the time heor she arrives?b. What is the system’s capacity?c. Assuming every staff member is able to do any of the three tasks, and average tasktimes are independent of who performs them, is it possible to increase the system’scapacity by reassigning tasks? If so, what change(s) would you recommend?