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 aproximate the binomial distribution.

0.7967

0.0606

0.0823

0.8577

Question

Mathematics

Drew Brown

2 April, 21:29

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 aproximate the binomial distribution.

0.7967

0.0606

0.0823

0.8577

+1

Answers (1)

Know the Answer?

Aliyah Vaughan · Answer 1

The best option is C. 0.0823mean = np = 48*1/4 = 12

SD = sqrt (npq) = sqrt (48 * 1/4 * 3/4) = 3

aplying continuity correction for using a continuous distribution for a discrete one,

"exactly 15" means 14.5 to 15.5

z1 = (14.5-12) / 3 = 0.833, z2 = (15.5-12) / 3 = 1.167

P (0.833 < z < 1.167) = 0.0808