A true-false examination has 48 questions. June has probability 3/4 of answering a question correctly. A passing score is 30 or more correct answers. Determine the probability that June passes the exam.

References

Doyle, Peter G. (2006). "Grinstead and Snell's Introduction to Probability" (PDF). Retrieved June 6, 2024.

Solution: E

By the central limit theorem, June's score is approximately normally distributed with mean 48*3/4 = 36 and variance 48 * 3/4 * 1/4 = 9. Therefore the probability that June passes the exam is approximately equal to the probability that a standard normal variable exceeds (30-36)/3 = -2. This is approximately equal to 0.9773.