Question

The heights of adult men in America are normally distributed, with a mean of 69.3 inches and a standard deviation of 2.66 inches. The heights of adult women in America are also normally distributed, but with a mean of 64.7 inches and a standard deviation of 2.56 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

For men

Mean = 69.3,

S.D = 2.66

For Women

Mean = 64.7,

S.D = 2.56

a) If a man is 6 feet 3 inches tall, what is his z-score is 2.12.

x = 6*12 + 3 = 75

By applying normal distribution:-

z = 2.12

c ) If a woman is 5 feet 11 inches tall, what is her z-score is 2.57.

x = 5*12 + 11 = 71

By applying normal distribution:-

z = 2.57

e ) The 5 foot 11 inch American woman is relatively taller because her z-score is greater than the -score for men.