A student answers all 48 questions on a multiple-choice test by guessing. Each question has four possible answers, only one of which is correct. Find the probability that the student gets exactly 15 correct answers. Use
The normal distribution to approximate the binomial distribution.
A)0.0823
B)0.8577
C)0.7967
D)0.0606

Question

Quizplus · Accepted Answer

The probability of guessing a correct answer is 0.25. The mean (μ) is 48 * 0.25 = 12, and the standard deviation (σ) is sqrt(48 * 0.25 * 0.75) ≈ 3. The z-score for 15 is (15 - 12) / 3 = 1. Using the standard normal distribution table, the probability of getting exactly 15 correct answers is approximately 0.0823.

A Student Answers All 48 Questions on a Multiple-Choice Test