Question

The heights of women aged 20 to 29 follow approximately the N(64, 2.72) distribution. Men the same age have heights distributed as N(69.3, 2.84). What percent of young men are shorter than the mean height of young women?

Answer 1

The z-score for men at 64 inches is:
$z=\frac{64-69.3}{2.84}=-1.866$
Using a standard normal distribution table, we can see that the cumulative probability for a z-score of -1.866 is 0.031.
The answer is 3.1%.