Final answer:
You and your friend will come out of the coffee shop at 9:12 a.m.
Step-by-step explanation:
To determine when you and your friend will come out of the coffee shop, we need to consider the interarrival time and service time. The interarrival time is the time between two successive arrivals, which is given as 3 minutes. The service time is the time taken to serve each customer, which is given as 9 minutes. Since you and your friend ordered different beverages, we can assume that the time taken to serve both of you is 9 minutes.
The first customer arrives at 9 a.m., and their service time is 9 minutes. The second customer (your friend) arrives 3 minutes later, at 9:03 a.m., and their service time is also 9 minutes. So, you and your friend will come out of the coffee shop at 9:12 a.m. (9 a.m. + 9 minutes + 3 minutes = 9:12 a.m.), which corresponds to option a) 9:12 a.m..