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Question

The heights of adult men in America are normally distributed, with a mean of 69.4 inches and a standard deviation of 2.65 inches. The heights of adult women in America are also normally distributed, but with a mean of 64.2 inches and a standard deviation of 2.57 inches.

a) If a man is 6 feet 3 inches tall, what is his z-score (to two decimal places)?

z = 

b) If a woman is 5 feet 11 inches tall, what is her z-score (to two decimal places)?

z = 

c) Who is relatively taller?

1. The 6 foot 3 inch American man
2. The 5 foot 11 inch American woman

Answer 1

Z-score means how many standard deviations away your number is from the mean.

Here:

Man 6'3"=75" (75-69.4)/2.65 = 2.11 (z-score)

Woman 5'11" = 71" (71-64.2)/2.57 = 2.65 (z-score)

The woman is relatively taller, as indicated by her higher z-score.