Question: A professor sits in his plush office and answers questions from his students the afternoon before the final exam. His class is a mass lecture of 350 students, so he keeps socialization to a minimum and concentrates on providing explanations as quickly as possible. On average, he can answer one question per minute and students arrive at his office every 3 minutes. Student arrivals are Poisson distributed, each student has only one question, and answer times are exponentially distributed.

a) What fraction of his time is the professor spending answering questions?

b) What is the average number of students waiting outside his office?

c) What is the average time a student spends in line outside the professor’s office?

d) What is the probability that less than three students are waiting outside the office?

e) This professor has a graduate assistant. If this assistant is in the office and helps the professor with answering questions at the same pace as professor, how long in average students spend waiting outside the office? What will be the probability that more than one student is waiting there?