Patients arrive at the emergency room of a hospital according to a Poisson process. A patient is classified into one of three types: high priority (i.e., a life is at stake), medium priority (i.e., the patient might be in pain but his or her life is not threatened), and low priority. On an average day, there are approximately 10 arrivals per hour. One-fifth of the arrivals are high priority, three-tenths are medium priority, and one-half are low priority. All registration matters are handled by a single clerk. The time to register a patient is exponentially distributed with a mean of 5.5 min (regardless of the classification of the patient). 

What is the average time to complete the registration of an arbitrary patient? (Assume that there is no preemption.)

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