A business school professor answers all the emails sent by his students on a first-come first-served basis. A few hours before the midterm exam, he receives an average of one student email every 18 minutes. Email inter-arrival times are exponentially distributed. Checking his email is the professor’s first priority during these hours, therefore he doesn’t carry out any other tasks whenever there are unanswered student emails in his in-box. It takes him 15 minutes to read and reply to each of these emails, and the variability of these two tasks combined is negligible. (a) [2] How long (in minutes) does it take on average for a student to receive a reply (i.e., from the time the email arrives to the professor’s in-box until he clicks the “send” button to reply)? (b) [2] What is the average number of unopened student emails in the professor’s in-box at any given time during these hours?