Hospital Systems, Inc (HSI)

The emergency room at HSI serves patients who arrive according to a Poisson distribution at the rate of 9 per hour.  Treatment takes an average of 6 minutes and the treatment times can be considered to follow an exponential distribution.  What is the

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(a)  minimum number of doctors required so that at least 70% of the arriving patients can receive treatment immediately?

(b)  minimum number of doctors required so that the average time a patient waits for treatment is no more than 30 minutes as advertised?  No more than 15 minutes?

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