"ahmadmadoff - what do you mean, the probability for getting above 18 is higher. Are you talking about the sum of the cumulative probabilities from 0-17 vs 19-54? what language was your code in anyway? " thats in VB.net, not the fastest lang for calculation but if you have no programing experience and you have 10 free hours you can pick up a book on vb.net or search online and learn enough to model anything finance… the syntax is very straight forward, almost like “human talk” but since your asking what lang, your are probably an experienced programmer, so this would apply to other people out there… during the CFA program I did tens of simulations to convince myself of some concepts, awsome tool to learn
you would probably get more than 33% of the guesses correct assuming you can eliminate one of the wrong answers on some of them.
How about we improve our threshold to get higher confidence? If you can answer 71/120 questions correct, you will then only need 13 more to pass. If you randomly guess on the remaining 49 questions, you will expect to get 16, and per binomial, have an 80% chance of getting the 13 needed. And, for large n, and high enough p, you CAN use the normal distribution to approximate. In this case, the 80% low end normal approximation is 13.56. Close! The distribution of outcomes is pretty symmetric around the expected Want to be 90% confident? Answer 73 correct. You can obtain these results using the Binomdist function in excel pretty easily. It allows for cumulative as well, to check confidence levels.