The heights of adult men in America are normally distributed, with a mean of 69.2 inches and a standard deviation of 2.66 inches.

Question

The heights of adult women in America are also normally distributed, but with a mean of 64.3 inches and a standard deviation of 2.58 inches.

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

z = ________

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)?

z =_________

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

Use: z-score = (x - μ)/σ

Convert the height to inches: x_man = 6 ft 3 in. = 6(12) + 3 = 75 in.

z_man = (75 - 69.2)/2.66 = 2.18 --> from a z-table --> .9854(100) = 98.54%

Convert the height to inches: x_woman = 5 ft 11 in. = 5(12) + 11 = 71 in.

z_woman = (71 - 64.3)/2.58 = 2.60 --> from a z-table --> .9953(100) = 99.53%

Answers:

a) z_man = 2.18

b) 98.5% of men are shorter

c) z_woman = 2.60

e) a 5 ft 11" American woman is relatively taller than a 6 ft 3" American man because the percentage of women shorter than her is 99.5% while the percentage of men shorter than him is 98.5%.