A true-false test of 20 questions is given to 10,000 students. If all the students guess on each question, how many students would you expect to get 17 or more questions correct?
A) 0.0013
B) 11
C) 13
D) 0.0011

Question

Quizplus · Accepted Answer

This is a binomial distribution problem with n = 20, p = 1/2, and N = 10,000. To find the number of students who get 17 or more questions correct, we can use the normal approximation to the binomial distribution with mean μ = np = 10,000*1/2 = 5000 and standard deviation σ = sqrt(np(1-p)) = sqrt(5000*1/2*1/2) = 50.5. We want to find P(X ≥ 17) = P(Z ≥ (17-16)/50.5) = P(Z ≥ 0.0198) = 0.4929, where Z is a standard normal random variable. Therefore, the expected number of students who get 17 or more questions correct is 0.4929*10,000 = 4,929. Since this is between 1% and 10% of the total number of students, we can reasonably assume that the normal approximation is appropriate. The closest answer choice is C, 13.

A True-False Test of 20 Questions Is Given to 10,000