This week, you are visiting a GSO grocery store in a rural town of Quebec to see if you could increase their customer satisfaction. During the three days you have been here, you have noticed that customers seem to be waiting a long time to pay for their groceries. It is a small local grocery store with only one cashier. The store is open daily from 8 a.m. to 6 p.m. On average, it takes the cashier 6 minutes to serve a client (the service time follows an exponential distribution). In the three days you have been in the store, you have counted an average of 80 clients each day and their arrival rate follows a Poisson distribution.

a) What are the arrival rate and service rate in the situation described above?

b) What is the average number of clients in the waiting line and the average time waiting in line?

c) What is the average total time spent in the system? Is this answer coherent with those given in a)? Justify.