WORKSHEET 7 THE OVERWORKED LECTURER

A lecturer teaching a simulation class of 15 students gives a homework assignment every class meeting and these assignments are collected at the beginning of the next class. The number of students completing the day's assignment follows a discrete probability distribution with probabilities listed in the table below.

The lecturer grades the assignments during office hours, which are scheduled for 90 minutes after class each day. The time to review an assignment follows a uniform distribution with a minimum of 2 minutes and a maximum of 3 minutes. Students may also make appointments to see the lecturer during office hours; visits are given a higher priority than assignments but the lecturer finishes grading the current assignment before helping the student. The lecturer schedules appointments with three to seven students per day (with equal probability for each number in the range) at 15 minute intervals starting at the beginning of office hours. Of the students who schedule appointments, 10% typically do not show up. The time that the lecturer spends with each student is triangular distributed (5, 10, 20 mins.).

Simulate the operation of a days office hours, collecting statistics on the time required to complete the days tasks (grading papers, seeing students), the average time students wait to see the lecturer and the percentage of time spent by the lecturer on each of the two tasks.

Probability | Number of students completing
0.2 | 11
0.2 | 12
0.3 | 13
0.1 | 14
0.2 | 15