Question

The heights of women aged 20 to 29 are approximately normal with mean 64 inches and standard deviation 2.7 inches. Men the same age have mean height 69.3 inches with standard deviation 2.8 inches. What are the z-scores for a woman 5'11" tall and a man 5'4" tall?

Answer 1

The z-score is the number of standard deviations of a value x from the mean:

... z = (x -μ)/σ

For the woman ...

... z = (71 -64)/2.7 ≈ 2.59 . . . woman's z-score

For the man ...

... z = (64-69.3)/2.8 ≈ -1.89 . . . man's z-score