("z-score") of the height

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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; GMAT Score:760

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

Made Up

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Sanjeev K Saxena
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Source: Beat The GMAT — Problem Solving | Tue Aug 14, 2012 2:49 am

Jim@StratusPrep: MBA Admissions Consultant; Posts: 2278; Joined: Fri Nov 11, 2011 7:51 amFollowed by: 266 members; Location: New York; Thanked: 660 times; GMAT Score:770

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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Brent@GMATPrepNow: GMAT Instructor; Posts: 16206; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

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.

Cheers,
Brent

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truplayer256: Master | Next Rank: 500 Posts; Posts: 392; Joined: Thu Jan 15, 2009 12:52 pm; Location: New Jersey; Thanked: 76 times

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.

sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; GMAT Score:760

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?

The mind is everything. What you think you become. –Lord Buddha

Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001

www.manyagroup.com

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