1. Bivariate Normal Distribution Problem

I am little bit confused with the conditional probabilities in the following problem.

The correlation coefficient between the heights of husbands and wives is 0.70 and the male height is 5 feet 10 inches with standard deviation 2 inches, and the mean female height is 5 feet 4 inches with standard deviation 1.5 inches. Assuming a bivariate normal distribution, what is the best guess of the height of a woman whose husband's height is 6 feet? Find a 95% prediction interval for her height.

The joint pdf f(x, y) can be constructed easily from the given data. Now find $f(y | x) = \frac{f(x, y)}{f_X(x)}$ where $f_X(x)$ is the marginal pdf of X and substitute x = 6 feet.