Question

The heights of adult men in America are normally distributed, with a mean of 69.3 inches...

The heights of adult men in America are normally distributed, with a mean of 69.3 inches and a standard deviation of 2.63 inches. The heights of adult women in America are also normally distributed, but with a mean of 64.1 inches and a standard deviation of 2.54 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
• The 6 foot 3 inch American man

Solution :

Given that ,

mean = = 69.3 in. (men)

standard deviation =  = 2.63 in.

x = 75

Using z-score formula,

z = x - /

z = 75 - 69.3 / 2.63

z = 2.17 ( men)

mean = = 64.1 in. (women)

standard deviation =  = 2.54 in.

x = 71

Using z-score formula,

z = x - /

z = 71 - 64.1 / 2.54

z = 2.72 ( women)

c) The 5 foot 11 inch American woman, because American women z-score 2.72 is bigger than American men z-score 2.17

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