Question

A history professor decides to give a 15-question true-false quiz. She wants to choose the passing grade such that the probability of passing a student who guesses onevery question is less than 0.10. What score should be set as the lowest passing grade?

Answer 1

So you can say this is a binomial problem. You have only 2 outcomes, that is pass or fail. you want the probability to be less than or equal to 10%.

Well .. 9/15 is a passing grade right? its a 60 i.e. D-. so that's your bar to set for the problem. You figure out the probability of passing first ofgetting a 60.

15C9(.5)^9(.5)^6=.1527404785 ... you want THAT result to be .1 or less right?! so Change the scale (the 9/15) to get it below the .1527404.. guess andcheck works pretty well here..

(reminder that the binomial formula is NCn (p)^n(p)^N-n {N= total problems, n= problems you have correct, and p= chances of getting a problem right)

.. if 10/15 is the new pass score.. you already have a probability that's less then 10% .. (it comes out to .091644) formula is 15C10(.5)^10(.5)^5 =.091644. so you would make the pass score 10/15 (or above if you were a jerk)

HOWEVER this means you can also MAKE the test EASIER by making the passing score =5/15 with probability of 15C10(.5)^5(.5)^10 [still equals .091644] andstill give those guessers a Less than 10% chance of passing.

The best I can give you man.