Awoman insists that she will never marry a man as short as or shorter than she, knowing that only one man in 400 falls into this category. assuming a mean height of 69 inches for men with a standard deviation of 2.5 inches (and a normal distribution), approximately how tall is the woman?

The woman is 61.5 inches tall.

This question is essentially asking for how many standard deviations the woman's height is away from the mean men's height.

Only 1 in 400 (or 0.25%) of men is shorter than our picky homegirl. If you think of a normal distribution of men's heights, this is the extreme left tail end. As a rule of thumb, +/- 3 standard deviations around the mean captures 99.5% of a population, leaving 0.5% outside of the interval (so, only 0.25% on each end). So we know that our girl refuses to marry anyone lower than -3 standard deviations from the mean.

All that's left is to plug in the given mean and SD:

69 -3(2.5) = 61.5 inches