Use the Central Limit Theorem Approximation to answer the following:
(a) A multiple-choice exam has 50 questions. Suppose the probability of getting each question correct is p = 0.8. independent of the other questions. If the cutoff for an “A” grade is 90% (that is, at least 45 correct), what is the probability of getting an “A”?
(b) A multiple-choice exam has 100 questions. Suppose the probability of getting each question correct is p = 0.8, independent of the other questions. If the cutoff for an “A” grade is 90% (that is, at least 90 correct), what is the probability of getting an “A”? Why is this different than the answer to part (a)?
(c) A multiple-choice exam has 100 questions. 50 of the questions have p = 0.7. and the remaining 50 questions have p = 0.90. If the cutoff for an “A” grade is 90%, what is the probability of getting an “A”? Why is this exam easier (or harder) than the one in pan (b)?
(d) Repeat the calculations in (a) and (b) using the “continuity correction”. Does this make much of a difference in your results?
