49. Multiple-Choice Exam. Consider a multiple-choice examination with 50 questions. Each question has four possible answers. Assume that a student who has done the homework and attended lectures has probability .75 of answering any question correctly.

a. A student must 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?

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?

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?

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 30 or more questions correctly and pass the examination?

53. Waiting in Line at Kroger. Do you dislike waiting in line? Supermarket chain Kroger has used computer simulation and information technology to reduce the average waiting time for customers at 2300 stores. Using a new system called QueVision, which allows Kroger to better predict when shoppers will be checking out, the company was able to decrease average customer waiting time to just 26 seconds (InformationWeek website).

b. What is the probability that a customer will have to wait between 15 and 30 seconds?

c. What is the probability that a customer will have to wait more than 2 minutes?

d. What is the probability that a customer waits less than 1 minute in line?