Question

A multiple-choice quiz has 200 questions, each with 4 possible answers of which

only 1 is correct. Then the probability that sheer guesswork yields more than 30

correct answers for the 80 of the 200 problems about which the student has no

knowledge is equal to

		0.0034
		0.0032
		0.0043
		None

Answer 1

Here the quiz has 200 questions

each with 4 possible answers of which 1 is correct.

Here total number of problems that student has no idea = 30

so here sample proportion = 1/4

E[x] = np = 80 * 0.25 = 20

SD[x] = sqrt(np(1-p)) = sqrt[80 * 0.25 * 0.75) = 3.873

so we have to find

P(x > 30) = BINOMDIST(x > 30 ; n = 30; p = 0.25) = 1- NORMSDIST(x <= 30.5; n = 30 ; p = 0.25)

Z = (30.5 - 20)/3.873 = 2.711

P(x > 30) = 1 - P(Z < 2.711) = 1 - 0.9966 = 0.0034