A true-false examination has 48 questions. June has probability 3/4 of answering a question correctly. April just guesses on each question. A passing score is 30 or more correct answers. Compare the probability that June passes the exam with the probability that April passes it.
June’s probability of passing the exam =>
1 - pnorm(30.5, mean=48*3/4, sd=sqrt(48*3/4*1/4))## [1] 0.9666235April’s probability of passing the exam =>
1 - pnorm(30.5, mean=48*1/2, sd=sqrt(48*1/2*1/2))## [1] 0.03030098