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("z-score") of the height

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("z-score") of the height

by sanju09 » Tue Aug 14, 2012 2:49 am
To convert a value to a Standard Score ("z-score"), first subtract the Arithmetic Mean from the value, then divide the result by the Standard Deviation. 95 percent of students at a school are between 1.1 meter and 1.7 meter tall. Assuming this data is normally distributed and that in the same school one of the student is 1.85 meter tall, what is the Standard Score ("z-score") of the height of this student?
A. 1
B. 1.5
C. 2
D. 2.5
E. 3



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by Jim@StratusPrep » Tue Aug 14, 2012 4:51 am
You will never see a z-score question on the GMAT. It will pop up in your first year stats class, but not the GMAT.
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by Brent@GMATPrepNow » Tue Aug 14, 2012 7:06 am
I agree with Jim. You'll never see the term "z-score" on the GMAT.
However, you will find this concept hidden in questions featuring "units of standard deviation" (like this question: https://www.beatthegmat.com/standard-dev ... 85292.html) .

So, rather than say that a certain value has a z-score of -2, we might say that a certain value is 2 units of standard deviation below the mean. They both have the same meaning.

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by truplayer256 » Wed Aug 15, 2012 4:41 am
This question is unlikely on the GMAT but I'll definitely go ahead and take an attempt at it. This problem follows something known as the normal distribution and the 68-95-99.7 rule. This rule states that area under the curve 1 SD away covers 68% of the area, and similarly, area under the curve 2 SD away covers 95% of the area. In this problem, let m be the mean and s be the standard deviation:

m-2s=1.1
m+2s=1.7

m=1.4
s= 0.15

z-score for 1.85 = (1.85-1.4)/0.15 = 3

Choose E.
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by sanju09 » Wed Aug 29, 2012 11:44 am
Hi Jim and Brent, thanks for the useful feedback. What would you say about the questions pertaining to "defined functions" on the GMAT where a temporary definition is sufficient no matter how space invader is that to many?
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