Assume that males have a mean height of 69.1 in. with a standard deviation of 2.9 in., and females
Have a mean height of 63.7 in. with a standard deviation of 2.7 in. Based on Z scores, would a 5'6"
Male or a 5'2" female be taller compared to the rest of their gender?
A)female
B)male

Question

Quizplus · Accepted Answer

To compare the two heights based on their respective genders, we need to convert them to Z-scores.

For the 5'6" male: 
1. Convert 5'6" to inches: 5 ft * 12 in/ft + 6 in = 66 in 
2. Calculate the Z-score: 
(Z-score) = (observed value - population mean) / standard deviation 
= (66 - 69.1) / 2.9 
= -1.07

For the 5'2" female: 
1. Convert 5'2" to inches: 5 ft * 12 in/ft + 2 in = 62 in 
2. Calculate the Z-score: 
(Z-score) = (observed value - population mean) / standard deviation 
= (62 - 63.7) / 2.7 
= -0.63

A negative Z-score means the observed height is below the average for their gender. Therefore, the female with a Z-score of -0.63 (5'2" height) is less below the average height for females than the male with a Z-score of -1.07 (5'6" height) compared to the average height for males. Therefore, the female is relatively taller compared to the rest of their gender.

Assume That Males Have a Mean Height of 69