Question

The heights of adult men in America are normally distributed, with a mean of 69.7 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 2.55 inches.

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

b) What percentage of men are SHORTER than 6 feet 3 inches? Round to nearest tenth of a percent.

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

d) What percentage of women are TALLER than 5 feet 11 inches? Round to nearest tenth of a percent.

e) Who is relatively taller: a 6'3" American man or a 5'11" American woman? Defend your choice in a meaningful sentence.

Answer 1

(a) The z-score for men 6 feet 3 inches tall

= (75 - 69.7)/2.65 = 2

(b) Percentage of men shorter than 6 feet 3 inches

= P(Z < 2) = 0.9772 = 97.72%

(c) The z-score for women 5 feet 11 inches tall

= (71 - 64.2)/2.55 = 2.667

(d) Percentage of women taller than 5 feet 11 inches

= P(Z > 2.667)

= 0.0038 = 0.38%

(e) A 5'11" American woman is relatively taller as compared to a 6'3" American man

Since the z score for the height of woman is higher and hence have a smaller right tail