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# standard deviation

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Director
Joined: 25 Oct 2008
Posts: 591
Location: Kolkata,India

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22 Jul 2009, 22:03
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If the mean on the exam is 530 and the standard deviation is 110,what percent of the test takers score between 420 and 750?

STUMPED!
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Senior Manager
Joined: 23 Jun 2009
Posts: 357
Location: Turkey
Schools: UPenn, UMich, HKS, UCB, Chicago

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22 Jul 2009, 22:30
What is the distribution type? Normal ? If normal what is the skewness and etc. We can only infer that it want us the distribution of -1 st.dev & + 2 st.dev. If this is a normal distribution with all variables standart, we can say that 0,4772 (z=2) + 0,3413 (z=1) = 0,8185 = %82
Director
Joined: 01 Apr 2008
Posts: 872
Name: Ronak Amin
Schools: IIM Lucknow (IPMX) - Class of 2014

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22 Jul 2009, 22:54
maliyeci wrote:
What is the distribution type? Normal ? If normal what is the skewness and etc. We can only infer that it want us the distribution of -1 st.dev & + 2 st.dev. If this is a normal distribution with all variables standart, we can say that 0,4772 (z=2) + 0,3413 (z=1) = 0,8185 = %82

can you pls explain further ? how do you come up with these figures?
I am not much into statistics as such
Senior Manager
Joined: 23 Jun 2009
Posts: 357
Location: Turkey
Schools: UPenn, UMich, HKS, UCB, Chicago

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22 Jul 2009, 23:18
This is one of the main concepts of basic statistics.
420=530-110=530-1.std.dev
So z1=(530-420)/110=1 (z is a term used for showing how many std. devs. far away from mean).
z2=(750-530)/110=2
After that we use normal normal distribution tables. You can find a table by googling. Put z's. z1 shows the left side, z2 shows the right side. Summing them, we find the total percentage.
Manager
Joined: 15 Apr 2008
Posts: 50
Location: Moscow

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22 Jul 2009, 23:22
Economist wrote:
maliyeci wrote:
What is the distribution type? Normal ? If normal what is the skewness and etc. We can only infer that it want us the distribution of -1 st.dev & + 2 st.dev. If this is a normal distribution with all variables standart, we can say that 0,4772 (z=2) + 0,3413 (z=1) = 0,8185 = %82

can you pls explain further ? how do you come up with these figures?
I am not much into statistics as such

Those are properties of normal distribution from http://en.wikipedia.org/wiki/File:Standard_deviation_diagram.svg
You can also check http://en.wikipedia.org/wiki/Normal_distribution
But, actually, GMAT doesn't check this knowledge.
Director
Joined: 25 Oct 2008
Posts: 591
Location: Kolkata,India

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23 Jul 2009, 01:24
Exactly guys,I got this question off the new PR 1012 and they have solved it exactly as the curve has been shown.I have'nt come cross such questions before.Do i need to learn it??Will it be tested on the GMAT??
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Senior Manager
Joined: 23 Jun 2009
Posts: 357
Location: Turkey
Schools: UPenn, UMich, HKS, UCB, Chicago

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23 Jul 2009, 01:31
But some datas are missing. e.g. What is skewness? What is kurtosis?
GMAT Tutor
Joined: 24 Jun 2008
Posts: 1346

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23 Jul 2009, 03:15
Normal distributions are *not* tested on the GMAT. The question in the post above can't be answered without more information, and if you need to use details of the normal distribution to answer it, it is not a realistic test question.
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Senior Manager
Joined: 18 Jun 2009
Posts: 356
Location: San Francisco

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23 Jul 2009, 08:35
IanStewart wrote:
Normal distributions are *not* tested on the GMAT. The question in the post above can't be answered without more information, and if you need to use details of the normal distribution to answer it, it is not a realistic test question.

How are we sure that such questions are not tested in GMAT? when the source is from Princeton Review who are into GMAT from decades.
GMAT Tutor
Joined: 24 Jun 2008
Posts: 1346

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23 Jul 2009, 09:08
gmanjesh wrote:
IanStewart wrote:
Normal distributions are *not* tested on the GMAT. The question in the post above can't be answered without more information, and if you need to use details of the normal distribution to answer it, it is not a realistic test question.

How are we sure that such questions are not tested in GMAT? when the source is from Princeton Review who are into GMAT from decades.

Trust whoever you like, but the GMAT only tests statistics of finite sets. Normally distributed sets are by definition infinite, so can't appear on the GMAT (finite sets can be at best 'approximately normal'), and the handful of questions that have been posted here recently about finite "normally distributed" sets are based on a misunderstanding of statistics.
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Manager
Joined: 05 Jun 2009
Posts: 75

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23 Jul 2009, 09:46
Provided the distribution is normal, just memorize the empirical rule, really kind of useful. 1 stdev of mean = 68% 2, = 95% 3 =99.7

so for the problem

100-68= 32 / 2 (its two tailed = 16% score below 530)
100-95=5 / 2 (its two tailed = 2.5% score above 750)

2.5+16 = 18.5 (not scoring within that rage and... 100-18.5 = 81.5 ~~82 which are those encompassed in that range.

SF
Re: standard deviation   [#permalink] 23 Jul 2009, 09:46
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