Question

The heights of adult men in America are normally distributed, with a mean of 69.3 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 64.2 inches and a standard deviation of 2.59 inches. If a man is 6 feet 3 inches tall, what is his z-score (to 4 decimal places)? z = If a woman is 5 feet 11 inches tall, what is her z-score (to 4 decimal places)? z = Who is relatively taller? The 5 foot 11 inch American woman The 6 foot 3 inch American man

Answer 1

For a man with 6 feet 3 inches = 75 inches tall
z = (x - μ)/σ
z = (75 - 69.3)/2.66 = 2.1429

for a woman with 5 feet 11 inches = 71 inches tall
z = (x - μ)/σ
z = (71 - 64.2)/2.59 = 2.6255

Woman is relatively taller