Question

A multiple-choice examination consists of 75 questions, each having possible choices a, b, c, and d. Approximate the probability that a student will get more than 18 answers correct if he randomly guesses at each answer. (Note that, if he randomly guesses at each answer, then the probability that he gets any one answer correct is 0.25.) Use the normal approximation to the binomial with a correction for continuity. Round your answer to at least three decimal places. Do not round any intermediate steps.

Answer 1

Sample size n= 75. Success probabilily p= q=1-p- the Binomial distribution using Plxav)-()pa. LA=pp = 75-16). = 18-75 Mean SD npq -J75() -14.0625. = 3:15. using the Normal Approximation, PC More than 18) = P(x218) = P(xu 18-18.75 3.75 = P (27,-0.2) =1-P (25.0.2) =1-(1-P (250.2)) = P(220.2) -0-5793.