Statistical help

Question

Could someone help me with this answer!!

 

One of the tallest living man has a high of 246 cm. One of the tallest living women is 234 cm tall. Heights of men have a mean of 171 cm and a standard deviation of 7 cm. Heights of women have a mean of 160 cm and the standard deviation of 8 cm. Relative to the population of the same gender who is taller?

Answer 1

Let's assume both populations are normal so M ∼ N(171,7²) and W ∼ N(160,8²)

 

The relative statistical height of a person can be taken as his z-score.

 

The z-score for the tallest man is

 

z = (246 - 171) / 7 = 75 / 7 = 10.714

 

The z-score for the tallest woman is

z = (234 - 160) / 8 = 74 / 8 = 9.25

 

The tallest man has the higher z-score and so is taller in the relative sense.