1. The problem statement, all variables and given/known data A multiple choice test consists of a series of questions, each with four possible answers. How many questions are needed in order to be 99% confident that a student who guesses blindly at each question scores no more than 35% on the test? 2. Relevant equations So I know that this is a binomial setting with p=0.25 and 'n' is what we are trying to solve for. for binomial, μ=n*p, σ=sqrt(n*p(1-p)) P(B(n,0.25)≤0.35*n)=0.99 And because of the binomial setting, we must use a correction factor, in this case '+0.5' Z= (x - μ)/σ 3. The attempt at a solution First I should say I know the answer is suppose to be n≥92 So how I start this problem is I use the standardizing formula Z= (x - μ)/σ which in this case would be Z= (0.35*n + 0.5 - n*0.25)/(sqrt(n*0.25*0.75) This simplifies to Z=(0.1*n + 0.5)/(sqrt(n)*sqrt(0.1875)) I think what I have done so far is correct. But where I get confused is finding a value for Z, I thought what I have to do is something like : P(B(n,0.25)≤0.35*n)=Φ((0.1*n + 0.5)/(sqrt(n)*sqrt(0.1875))) = 0.99 so, Φ((0.1*n + 0.5)/(sqrt(n)*sqrt(0.1875))) = 0.99 look up 0.01 on the table which gives me Φ(2.33)=Φ((0.1*n + 0.5)/(sqrt(n)*sqrt(0.1875))) and so I should be able to set those equal and solve for n: 2.33 = ((0.1*n + 0.5)/(sqrt(n)*sqrt(0.1875)) When I solve for n I get a quadratic formula but neither answers I get is the correct answer. Any help would be appreciated. Thanks!