standard deviation

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uptowngirl92: Master | Next Rank: 500 Posts; Posts: 447; Joined: Sun Apr 19, 2009 9:08 pm; Location: Kolkata,India; Thanked: 7 times; GMAT Score:670

by uptowngirl92 » Wed Jul 22, 2009 10:02 pm

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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Source: Beat The GMAT — Problem Solving | Wed Jul 22, 2009 10:02 pm

raghavsarathy: Master | Next Rank: 500 Posts; Posts: 166; Joined: Sat Apr 18, 2009 10:41 pm; Thanked: 9 times; GMAT Score:770

by raghavsarathy » Wed Jul 22, 2009 10:14 pm

[Edit my post..]

Initially took the % in each range as 10%.. Bad.. Just studied SD concepts again.

Hence changing the %

IMO - 81.8%

Since SD = 110

Mean -SD = 420 .. Between 420 and 530 we have 34.1% of sudents

Similarly between 530 and 750 we have a SD of 220 = 110*2. Hence 34.1 + 13.6 = 47.7 %

Hence 81.8 % of the students score between 420 and 750

Last edited by raghavsarathy on Wed Jul 22, 2009 10:40 pm, edited 1 time in total.

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bfman: Senior | Next Rank: 100 Posts; Posts: 63; Joined: Tue Mar 31, 2009 3:53 pm

by bfman » Wed Jul 22, 2009 10:19 pm

Don't we have to know the percentage as it corresponds to the deviation?

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Spaceman Spiff: Senior | Next Rank: 100 Posts; Posts: 54; Joined: Fri Apr 03, 2009 7:23 pm; Location: Los Angeles; Thanked: 1 times; GMAT Score:780

by Spaceman Spiff » Wed Jul 22, 2009 10:31 pm

68.2% of a normally distributed population falls within 1 standard deviation of the mean (34.1% on each side). 95.5% falls within two (additional 13.6% on each side). 2 SD of mean here is:

-2 -1 MEAN +1 +2

310 420 530 640 750

So we have 68.2+ 13.6 = 81.8%

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uptowngirl92: Master | Next Rank: 500 Posts; Posts: 447; Joined: Sun Apr 19, 2009 9:08 pm; Location: Kolkata,India; Thanked: 7 times; GMAT Score:670

by uptowngirl92 » Thu Jul 23, 2009 1:26 am

IS this concept tested on the GMAT??34%,14% and 2%?This question is from the new PR 1012 but I havent come across such questions before.Do we need to learn it?

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tohellandback: Legendary Member; Posts: 752; Joined: Sun May 17, 2009 11:04 pm; Location: Tokyo; Thanked: 81 times; GMAT Score:680

by tohellandback » Thu Jul 23, 2009 1:34 am

few questions:
1) How can you be sure that the distribution is normal?
because as far as I know the values you are taking are only valid for Normal distribution

2) so do we need to remember values for population distribution.

The powers of two are bloody impolite!!

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Spaceman Spiff: Senior | Next Rank: 100 Posts; Posts: 54; Joined: Fri Apr 03, 2009 7:23 pm; Location: Los Angeles; Thanked: 1 times; GMAT Score:780

by Spaceman Spiff » Thu Jul 23, 2009 1:46 am

The problem wasn't posted completely so I assumed normal distribution since it is a problem solving question, which means we must be able to solve it with the given information and the only way to do that is to assume normal distribution.

I am not sure if you need to know the values but I think (and I may be wrong) that 68% and 95% are "common knowledge". I remember having seen a few problems that required knowledge of the first and 2nd SDs.

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Ian Stewart: GMAT Instructor; Posts: 2623; Joined: Mon Jun 02, 2008 3:17 amFollowed by: 355 members; Location: Montreal; Thanked: 1090 times; GMAT Score:780

by Ian Stewart » Thu Jul 23, 2009 3:04 am

The question in the original post cannot possibly be answered - we have no idea how our data is distributed.

Incidentally, on the GMAT, no set is ever 'normally distributed' (you don't do stats on infinite sets on the GMAT), so you should never try to use rules you may know about normal distributions on GMAT questions. Any prep company question that relies on these rules is irrelevant to the GMAT. You don't even need to know what the phrase 'normally distributed' means for the test.

For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

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tohellandback: Legendary Member; Posts: 752; Joined: Sun May 17, 2009 11:04 pm; Location: Tokyo; Thanked: 81 times; GMAT Score:680

by tohellandback » Thu Jul 23, 2009 3:09 am

Ian Stewart wrote:The question in the original post cannot possibly be answered - we have no idea how our data is distributed.

Incidentally, on the GMAT, no set is ever 'normally distributed' (you don't do stats on infinite sets on the GMAT), so you should never try to use rules you may know about normal distributions on GMAT questions. Any prep company question that relies on these rules is irrelevant to the GMAT. You don't even need to know what the phrase 'normally distributed' means for the test.

Thanks Ian, that's what I thought.

The powers of two are bloody impolite!!

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