Squeak: I understand what you are asking now. I have no idea what the answer is. I double checked my math, and it is correct, and I double checked the z score and it is correct. There is .4992% to the left of the score, which means there is slightly less than a 1% chance of falling this far off the mean. Which means that it will happen about 1% of the time even with a quarter that is evenly weighted.
I frankly have no idea what the mistake I am making is.
Torah613: Squeak points out that the chances are in fact 1 in a thousand, while a z score of 3.16 gives us about a 1 in a hundred chance. Which makes absolutely no sense.
I don’t get it; I’ll ponder more tomorrow.