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:
(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?