Suggest a multiple-choice examination with 50 questions. Each question has four possible answers. Suppose that a student who has done the homework and attended lectures has a 75% probability of answering any question correctly. Use the normal approximation of the binomial probability distribution to answer the following questions.
a. A student should answer 43 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 (to 2 decimals)?
b. A student who answers 35 to 39 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 (to 2 decimals)?
c. A student must answer 30 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 (to 2 decimals)?
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 percentage of students who have not done their homework and have not attended class will answer 30 or more questions correctly and pass the examination (to 2 decimals)?