Question

The heights of adult men in America are normally distributed, with a mean of 69.2 inches and a standard deviation of 2.62 inches. The heights of adult women in America are also normally distributed, but with a mean of 64.6 inches and a standard deviation of 2.59 inches.

a) If a man is 6 feet 3 inches tall, what is his z-score?

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?

z =

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?

Answer 1

a)

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

b)

ans = 98.66

c)

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

d)

ans = 0.67%

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 99.33% while the percentage of men shorter than him is 98.66%.