Question 4. Many students in MTH203 will come to Annie's office hours in the coming Wednesday afternoon, say, 8 per hour (one by one), following Poisson distribution. Assume that on average, each student stays for 5 minutes, exponentially distributed. (1) Suppose for the coming Wednesday you do have a few questions but only available for at most 30 minutes during the entire office hour period, will you go then? (2) If she prefers to talk to students most of the time rather than being bored alone, Annie should be more patient and spend more time with each visit. So how long she should be with each visit (on average) in order to be busy at least 80% of the time? (3) Noticing that all the three lecturers of MTH203 actually hold office hours at the same time, list necessary assumptions and compute the average queue length in this case. (You are allowed to use online calculators but again, please attach snapshots.)