In a T-F exam with 100 questions, passing requires a score of at least 60. What is the approximate normal probability that a "guesser" will score at least 60 points?
A).0287
B).4713
C).0251
D).0377

Question

Quizplus · Accepted Answer

The probability of guessing correctly on any one question is 1/2. The probability of guessing correctly on at least 60 questions is the same as the probability of guessing incorrectly on at most 40 questions. The probability of guessing incorrectly on at most 40 questions is the sum of the probabilities of guessing incorrectly on 0, 1, 2, ..., 40 questions. The probability of guessing incorrectly on k questions is (1/2)^k * (1/2)^(100-k) = (1/2)^100. The sum of the probabilities of guessing incorrectly on 0, 1, 2, ..., 40 questions is (1/2)^100 * (1 + 1/2 + 1/4 + ... + 1/2^40) = (1/2)^100 * (1 - 1/2^41) = (1 - 1/2^41) = 0.0287.

In a T-F Exam with 100 Questions, Passing Requires a Score