booster vaccination shots against covid 19 were being administered at the Golden Grove Health Centre. Persons received their vaccination on a first come first serve basis. It took 6 minutes to vaccinate person ("jab a person) and see them out of the room. Only one doctor administered the vaccine. 2 persons arrived at the health centre every 10 minutes. Arrivals follow a Possion distribution while service time follows an exponential distribution.

a) What was the Utilization rate of the vaccination process at the health centre. 2 marks

b) What was the probability that no one is in the system 2 marks

c) Determine the average number of persons waiting to see the doctor 2 marks

d) Determine the average number of persons in the system 2 marks

e) On average how long will a person have to wait in line 2 marks

f) What is the average time a person spends in the system 2 marks

g) What is the probability there is 1 person getting the jab and 2 persons waiting 3 marks