Suppose your grade in a probability course depends on 10

Chapter 9, Problem 9.42

(choose chapter or problem)

Suppose your grade in a probability course depends on 10 weekly quizzes. Each quiz has ten yes/no que..stions, each v;,rorth 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 X i on quiz i is between 0 and 10. Your av10 erage score, X = I:i=l Xi/ 100 is used to determine your grade. Tl1e course grading has simple letter grades without any curve: A: X > 0.9, B: 0.8 < X < 0.9, C: 0.7 < X < 0.8, D: 0.6 < X < 0.7 and F : X < 0.6. As it happens, you are a borderline B /C student with p = 0.8. (a) What is the P MF of X i? (b) Use the central limit theorem to estimate the probability P [A] that your grade is an A. ( c) Suppose no'v that the course has "attendance quizzes." If you attend a lecture 'vith 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 X' = lOn + EI~, xi lOri + 100 is used to calculate your grade: A: X ' > 0.9, B: 0.8 < X' < 0.9, and so on. Given you attend ri attendance quizzes, use the central limit theorem to estimate P [A]. (d) Now suppase there are no attendance quizzes and your week 1 quiz is scored an 8. A fe,v hours after the week 1 quiz, you notice that a question 'vas marked incorrectly; your quiz score should have been 9. You appeal to the annoying prof 'vho 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].