E.1 Finding grades. In my statistics class, the final average is based on the following grading distribution:
| Presentations | Quizzes | Midterm 1 | Midterm 2 | Midterm 3 | Final Exam |
|---|---|---|---|---|---|
| 5% | 20% | 15% | 15% | 15% | 30% |
Suppose that Bob has an 83 quiz average, a 100 presentation average, and the following three midterm exam grades: 71, 85, 79. What is the lowest grade that Bob can get on the final exam and still finish with a final average of 80 (or higher) for the course?
E.2 Unusual dice. A six-sided die is manufactured so that it has two sides marked with the number six, and no side marked with the number one. The other sides are marked normally. What is the expected value of rolling this six-sided die? Assume that each side is equally likely to land on top.
E.3 Calculus Final Exam. Professor Abel, Professor Bernoulli, and Professor Cantor each teach one of the sections of calculus at a university. Prof. Abel’s class has 20 students, Prof. Bernoulli has 35 students, and Prof. Cantor has 45 students. If the average grade on the final exam was 72 in Prof Abel’s class, 78 in Prof. Bernoulli’s class, and 82 in Prof. Cantor’s class, then what is the average final exam grade for all of the students taking calculus?