A professor gives a 15 question truefalse quiz She wants to

A professor gives a 15 question true/false quiz. She wants to choose a passing grade such that the probability of passing a student who guesses on every question is less than 1/10. What should she set as the lowest passing grade?

Solution

let X be the number of current answers given

X follows binomial distribution

with n= 15 , p= 0.5 and q =0.5

standard deviation = sqrt(npq) = sqrt(15 * 0.5 * 0.5) = 1.9375

let k be lowest passing score

P(x>=a) = 0.1

=> 1- P(X < a) = 0.1

=> a = invnorm (0.9,7.5,1.9365) + 0.5

= 10.48

= 11