A high school guidance counselor has scheduled one-on-one meetings today with 10 seniors to discuss their college plans. Each meeting is scheduled for 20 minutes, with the first meeting set to start at 9:00 a.m. Due to their hectic class and extra-curricular schedules, not every student arrives on time, and not every meeting lasts exactly 20 minutes. The counselor knows the following from past experience: A student will be 10 minutes early 5% of the time, 5 minutes early 20% of the time, exactly on time 35% of the time, 5 minutes late 30% of the time, and 10 minutes late 10% of the time. The counselor further estimates that there is a 15% chance that a meeting will take only 15 minutes, 50% chance it will take exactly the planned time, 25% chance it will take 25 minutes, and 10% chance it will take 30 minutes.
Students are seen in the order in which they have been scheduled, regardless of when they arrive. However, a student arriving early can see the counselor as soon as the previous meeting ends. Use N replications to determine when the counselor will complete the last meeting.