A professor sits in his office and answers questions from his students the afternoon before the final exam. His class is a mass lecture of 350 students, so he concentrates on providing explanations as quickly as possible. On average, he can answer 60 questions an hour and students arrive at his office every five minutes. Student arrivals are Poisson distributed, each student has only one question and answer times are exponentially distributed.
a. What fraction of his time does the professor spend 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?