Booster vaccination shots against covid 19 are being administered at the Golden Grove Health Centre. Persons receive their vaccination on a first come first serve basis. It takes 5 minutes to vaccinate person ("jab a person) and see them out of the room. Only one doctor administers the vaccine. 10 persons arrive at the health centre every hour. Arrivals follow a Possion distribution while service time follows an exponential distribution.

a) What is the Utilization rate of the vaccination process at the health centre.

b) What is the probability that no one is in the system

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

d) Determine the average number of persons in the system

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

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

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

h) What is the probability there are more than 2 persons in the system