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.

• 0.90
• 0.92
• 0.94
• 0.96
• 0.98

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.