Question

The heights of adult men in America are normally distributed, with a mean of 69.8 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 64.4 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:

a)

For men , = 69.8 inches , = 2.66 inches

Consider a height 6 feet 3 inches

x = 6 feet 3 inches = (6 * 12) + 3 = 75 inches

Using z score formula ,

z = = (75 - 69.8)/2.66 = 1.95

z = 1.95

b)

For women , = 64.4 inches , = 2.56 inches

Consider a height 5 feet 11 inches

x = 5 feet 11 inches = (5 * 12) + 11 = 71 inches

Using z score formula ,

z = = (71 - 64.4 )/2.56 = 2.58

z = 2.58