Here's the problem statement...
A sample consisting of 48% men and 52% women is such that the height of men follows a normal distribution with mean 182cm and variance 7cm, and the height of women follows a normal distribution with mean 168cm and variance 5cm.
Given a person selected at random is between 174 and 175 cm tall what's the probability of that person being a women?
...I set the height of men as X~N(182, 7^2) and women as Y~N(168, 5^2). I calculated P(174 < Y < 175) / (P(174 < Y < 175) * P(174 < X < 175)) which gave me the wrong answer, 0.52. The answer is supposed to be 0.54.