A Finance professor created a multiple-choice examination with 100 questions for his students. Each question has five possible answers. Assume that a student who has done the homework and attended lectures has an 85% probability of answering any question correctly.
a. A student must answer 90 or more questions correctly to obtain a grade of A. What percentage of the students who have done their homework and attended lectures will obtain a grade of A on this multiple choice examination?
b. A student who answers 77 to 83 questions correctly will receive a grade of C. What percentage of students who have done their homework and attended lectures will obtain a grade of C on this multiple choice examination?
c. A student must answer 73 or more questions correctly to pass the examination. What percentage of the students who have done their homework and attended lectures will pass the examination?
d. If a student does not pass the examination but the student answers 28 or more questions correctly, the student can appeal to take another new examination. If pass, the highest grade can only be a passing grade, say D. Assume that a student has not attended class and has not done the homework for the course. Furthermore, assume that the student will simply guess at the answer to each question. What is the probability that this student will answer 28 or more questions correctly and have an opportunity to appeal to take another new examination?