I guess the range is then: 240!/(168!*72) * .25^168*.75*72 to .25^240.
.25^168 is so close to 0… you are looking at abject failure there…
I can do the exact answer in Mathematica if it would help. but Deoivre Laplace is really close. The idea is that a binomial r.v. is just the sum of bernoulli r.v.'s. In this case there are 240 of them. On yur CFA exams you’re willing to say n > 30 => normal and here we have 240 but you need a more exact answer?!
Look on the bright side. If you work reasonably hard then: 75% chance of getting each question right => P(Pass) = P(Z>-1.71) = 95.7% If you get up to 80%, then P(Pass) becomes P(Z>-3.79) = 99.9925% In fact, to have a 99% chance of passing, you need to target getting 76.6% of questions right. Aim for 80%, and you should be home free.