Question

the average 20 to 29 year old is 69.6 inches tall, with a standard deviation of 3.0 inches, while the average 20 to 29 year old woman is 64.1 inches tall, with a standard deviation of 3.8 inches. Who is relatively taller, a 75 inches man or a 70 inches woman?

Answer 1

Solution :

Given that ,

mean = = 69.6 ( man )

standard deviation =  = 3.0

x = 75

Using z-score formula,

z = x - /   

z = 75 - 69.6 / 3.0

z = 1.80 ( man )

mean = = 64.1 ( woman )

standard deviation =  = 3.8

x = 70

Using z-score formula,

z = x - /   

z = 70 - 64.1 / 3.8

z = 1.55 ( woman )

Man z - score is 1.80 more than woman z-score 1.55 so, man is relatively taller than woman