A professor holds six office hours per week. Demand for office hours varies wildly as reflected in this historical data.
The duration of time to answer questions varies independently from the actual demand. Question duration is reflected in this table.
Probability 0.5 0.05 0.1 0 0.05 0.05 0.1 0.1 0.05
# Students per 6 hours 0 1 2 3-9 10 11 12 13 14
Entries in the student demand and question duration tables that reflect a range in demand, i.e., 3-9 students per six hours or 4-9 minutes, should be treated as collapsed entries in the table. Thus, a question duration of 4 minutes has a 0.05 probability, a question duration of 5 minutes also has a 0.05 probability, and so on up through 9 minutes and a 0.05 probability.
This table contains random numbers for the number of students and the question duration for a 16-week period.
Week # Students Question Duration
Week 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
# Students 82 60 94 94 36 50 21 71 94 22 31 58 81 44 21 34
Duration 20 71 60 80 33 11 32 49 14 36 18 74 97 9 4 96
Use the question duration figure as the time required to answer questions for each student that week, so if three students arrive in week seven and the average duration is ten minutes, the total time spent answering questions that week is thirty minutes.
a) Based on the information in the Tables above, what is the total duration spent for answering questions during Week #11?
b) Based on the information in the Tables above, what is the highest time spent answering questions for all of the weeks?
Please show the interim calculations for probability, cumulative probability, and random number intervals for the # students and the duration of the questions.