Question

The heights of adult men in America are normally distributed, with a mean of 69.6 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 64.2 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 =

Answer 1

Solution :

Given that ,

a) mean = = 69.6

standard deviation =  = 2.63

x = 75

Using z-score formula,

z = x - /   

z = 75 - 69.6 / 2.63

z = 2.05

b) mean = = 64.2

standard deviation =  = 2.56

x = 71

Using z-score formula,

z = x - /   

z = 71 - 64.2 / 2.56

z = 2.66