I’ve been thinking about the idea of minimum passing score with randomness and quessing. Let’s say CFAI wants people to get 70% right on the exam for a pass (this could be any number). They also know that people do guess and they’ll have to compensate for it. We know that, if you know you will at least get 66 questions right, and guessed on the other questions, you’ll get around 70% - if everything is random. So, there is a confidence interval for 70%, it is set at 55% (66/120) + the lower bound of the 95% confidence interval of 18 correct with 1/3 randomness.
No need to calculate this, I just ran a monte carlo simulation with 100,000 runs. It’s around 11 questions for the lower bound of 18 questions correct. (the standard deviation of 18 correct questions is 3.46)
So, this means the minimum passing score would probably be around 64% (66+11=77, 77/120=64.17%) if they want people to pass with 70%
And yes, I know CFAI has their modified angoff, and people taking the exam to test questions, and the final say is up to them, but all of that aside, this IS the number.