3. An Industrial Engineering professor decides to vacation at the beach with his family. While the kids play, he observes an ice cream stand (called Ben's) a few yards away manned by one person. Over the afternoon he notices that, on average, there are about 9 customers in line (waiting or being served) and customers arrive about every 2/3 minutes. He also calculates that, on average, a customer spends about 5 minutes waiting in line before being served.

a. On average, how long does a customer spend at the stand?

b. On average, how long does it take to serve a customer?

c. When the professor got to the beach, he noticed another ice stand (called Jerry's) that seemed to have virtually no customers due to its location. He figures that he can walk about 3 miles/hour, and this other stand is about 1200 feet away from where he is sitting. When the professor decides to go get ice cream, he wants to spend the least amount of time, on average, doing so. What is the greatest number of people that can be at Ben's stand before the professor will choose to walk to Jerry's and back? State any assumptions.

d. Having nothing better to do, the professor has determined that standard deviation of the service time is roughly the same as the mean service time. Suppose a customer has been in service already for 1.5 minutes, what is their expected remaining service time?