Question

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 a 65% chance of answering any question correctly. (Round your answers to two decimal places.)

(a) A student must answer 44 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? Use the normal approximation of the binomial distribution to answer this question.

(b) A student who answers 34 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? Use the normal approximation of the binomial distribution to answer this question.

(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? Use the normal approximation of the binomial distribution to answer this question.

(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? Use the normal approximation of the binomial distribution to answer this question.

Answer 1

Answer a)

Thus, 0.06% of the students who have done their homework and attended lectures will obtain a grade of A on this multiple-choice examination.

Answer b)

Thus, 36.45% of students who have done their homework and attended lectures will obtain a grade of C on this multiple-choice examination

Answer c)

Thus, 81.31% of the students who have done their homework and attended lectures will pass the examination.

Answer d)

It is given that there is 65% chance of answering any question correctly for student  who has done the homework and attended lectures. Thus, for student who has not done the homework and attended lectures, the chance of answering any question correctly is 100-65 = 35%

The probability that this student will answer 30 or more questions correctly and pass the examination is 0.0002. If we round of the answer to 2 decimal place, the probability can be said to be zero. In other words, the possibility/probability of the student, who has not attended class and has not done the homework for the course, passing the examination is zero.