A pharmacy has started a special clinic where two pharmacists are giving flu shots to customers. Customers interested in receiving a shot visit the clinic following a Poisson process with mean rate of 8 customers/hour. For each customer, it takes a pharmacist, on average, 12 minutes to first complete all paperwork and then administer a shot. The service times are exponentially distributed.

First, suppose that each customer is randomly assigned to one of the two pharmacists on arrival. Before they can receive their shot, a customer needs to wait until the designated pharmacist finishes processing all previous customers allocated to them (even if the other pharmacist is waiting idly).

Question 1: How long does an average customer spend in the clinic (in minutes) (i.e., the total time including waiting in line, filling up paperwork, and receiving a shot)? If your answer is not an integer, provide at least three decimal places, e.g., 7.500.

Hint: Remember that each pharmacist is assigned half of the arriving customers!

NOTE: The answer already on course hero and ch*gg are incorrect. PLEASE don't use them to provide the solution!