Question

The heights of adult men in America are normally distributed, with a mean of 69.1 inches and a standard deviation of 2.67 inches. The heights of adult women in America are also normally distributed, but with a mean of 64.8 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)?

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?
The 5 foot 11 inch American woman? OR The 6 foot 3 inch American man?

Answer 1

Given that the heights of adult men in America are normally distributed, with a mean of = 69.1 inches and a standard deviation of = 2.67 inches. The heights of adult women in America are also normally distributed, but with a mean of = 64.8 inches and a standard deviation of = 2.56 inches.

a) So, the Z score for men is calculated as:

Where, X = 6 ft 3 inches = 6*12+3 = 75

so, The Z score is:

b) Here for women, the X is 5 ft 11 inches = 5*12+11 = 71 inches

so, the Z score is:

c) Those who will have the largest Z score will be relatively taller since women Z score = 2.42 is greater than man Z score hence the 5 foot 11-inch American woman is taller.