SOLUTION: If the difference between the heights of two persons is 15cm and the difference between their standard scores is 1.5, what is the standard deviation? Show your calculation.

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Question 1135972: If the difference between the heights of two persons is 15cm and the difference between their standard scores is 1.5, what is the standard deviation? Show your calculation.
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
If the difference between the heights of two persons is 15cm
That says: 
[1]   H%5B1%5D-H%5B2%5D=15

and the difference between their standard scores is 1.5,
 
That says: 
[2]   %28H%5B1%5D-mu%29%2Fsigma-%28H%5B2%5D-mu%29%2Fsigma=1.5

what is the standard deviation? Show your calculation.
We simplify [2]

%28%28H%5B1%5D-mu%29%29%2Fsigma-%28%28H%5B2%5D-mu%29%29%2Fsigma=1.5

Multiply both sides by s

%28H%5B1%5D-mu%29-%28H%5B2%5D-mu%29=1.5sigma

H%5B1%5D-mu-H%5B2%5D%2Bmu=1.5sigma

H%5B1%5D-cross%28mu%29-H%5B2%5D%2Bcross%28mu%29=1.5sigma

H%5B1%5D-H%5B2%5D=1.5sigma

Substitute for H1-H2 using [1],

15=1.5sigma

Divide both sides by 1.5

15%2F1.5=1.5sigma%2F1.5

10=sigma

Edwin