A hospital emergency department (ER) is currently organized so that all patients must register through an initial check-in process (there is almost...

A hospital emergency department (ER) is currently organized so that all patients must register through an initial check-in process (there is almost always a wait). Emergency patients, however, are admitted directly to the hospital without having to register. After registering, each patient waits to be seen by a doctor, sees the doctor, and then exits the ER process, either by being released or with admission to the hospital. 

Currently, 40 people per hour arrive at the ER, 10% of whom are admitted directly to the hospital without waiting. On average, 9 people are waiting to be registered and 36 are registered and waiting to see a doctor. The registration process takes, on average, 2 minutes per patient. The average time spent with a doctor is 30 minutes, during which 75% are treated and released; the rest are admitted to the hospital after seeing the doctor. Assume the process is stable. 

(Draw the process flow for the ER. Label all relevant measures (R, I, and T's). Show all work.

a) On average, how long does a patient stay in the ER if not directly admitted?

b) On average, how many patients are being examined by doctors? 

c) On average, how many patients are in the ER?