Suppose your grade in a probability course depends on 10 weekly quizzes. Each quiz has ten yes/no questions, each worth 1 point. The scoring has no partial credit. Your performance is a model of consistency: On each one-point question, you get the right answer with probability p, independent of the outcome on any other question. Thus your score Xi on quiz i is between 0 and 10. Your average score, X = ˆ‘10i=1 is used to determine your grade. The course grading has simple letter grades without any curve: A: X ‰¥ 0.9, B: 0.8 ‰¤ X (a) What is the PMF of Xi?
(b) Use the central limit theorem to estimate the probability P[A] that your grade is an A.
(c) Suppose now that the course has "attendance quizzes." If you attend a lecture with an attendance quiz, you get credit for a bonus quiz with a score of 10. If you are present for n bonus quizzes, your modified average

is used to calculate your grade: A: X' ‰¥ 0.9, B: 0.8 ‰¤ X' (d) Now suppose there are no attendance quizzes and your week 1 quiz is scored an 8. A few hours after the week 1 quiz, you notice that a question was marked incorrectly; your quiz score should have been 9. You appeal to the annoying prof who says "Sorry, all regrade requests must be submitted immediately after receiving your score. But don't worry, the probability it makes a difference is virtually nil." Let U denote the event that your letter grade is unchanged because of the scoring error. Find an exact expression for P[U].

10n 100