Question

The heights of adult men in America are normally distributed, with a mean of 69.1 inches and a standard deviation of 2.68 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 2.58 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 =

Answer 1

Solution :

Given ,

men

mean = = 69.1

standard deviation = = 2.68

x=75.6 inches (6.3feet)

using z-score formula

z =X -/

z=75.6-69.1/2.68

z=2.46

b.

woman

mean = = 69.1

standard deviation = = 2.68

x=61.32 inches (5.11feet)

using z-score formula

z =X -/

z=61.32 -69.1/2.68

z=-2.90