Question

In a certain​ city, the average​ 20- to​ 29-year old man is 69.8 inches​ tall, with a standard deviation of 3.2 ​inches, while the average​ 20- to​ 29-year old woman is 64.5 inches​ tall, with a standard deviation of 3.8 inches. Who is relatively​ taller, a​ 75-inch man or a​ 70-inch woman?

Find the corresponding​ z-scores. Who is relatively​ taller, a​ 75-inch man or a​ 70-inch woman? Select the correct choice below and fill in the answer boxes to complete your choice.

​(Round to two decimal places as​ needed.)

A.The​ z-score for the woman​, __ is smaller than the​ z-score for the man​, ___​, so she is relatively taller.

B.The​ z-score for the man​,__, is larger than the​ z-score for the woman​,__​, so he is relatively taller.

C.The​ z-score for the woman​,__, is larger than the​ z-score for the man​,___, so she is relatively taller.

D.The​ z-score for the man​,__​, is smaller than the​ z-score for the woman​,___, so he is relatively taller.

Answer 1

Answer :  

for man = x1 here μ1 = 69.8 and σ1 = 3.2  

for woman = x2 here μ2  = 64.5 and  σ2 = 3.8

## Find the corresponding​ z-scores. Who is relatively​ taller, a​ 75-inch man or a​ 70-inch woman?

## z score for man when x1 = 75

z = ( x1 - μ1) / σ1 = ( 75 - 69.8 ) / 3.2

= 1.625 ie 1.63 and

## z score for woman when x2 = 70

z = ( x2 - μ2 ) / σ2   = ( 70 - 64.5 ) / 3.8

= 1.447   ie 1.45  

## Select the correct choice below and fill in the answer boxes to complete your choice.

Answer :

here z score for man is larger than woman . correct option is ,

B.The​ z-score for the man​, 1.63, is larger than the​ z-score for the woman​, 1.45 ​, so he is relatively taller.