Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 19 Dec 2014, 21:09

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# Two different groups of test-takers received scores on the

 Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:
Manager
Joined: 13 Dec 2005
Posts: 64
Followers: 1

Kudos [?]: 3 [0], given: 0

Two different groups of test-takers received scores on the [#permalink]  22 Dec 2005, 20:44
Two different groups of test-takers received scores on the GXYZ standardized test. Group A's scores had a normal distribution with a mean of 460 and a standard deviation of 20. Group B's scores had a normal distribution with a mean of 520 and a standard deviation of 40. If each group has the same number of test-takers, what fraction of the test-takers who scored below 440 belonged to Group B?

A) 1/9
B) 1/8
C) 1/6
D) 4/17
E) 4/21
SVP
Joined: 05 Apr 2005
Posts: 1733
Followers: 4

Kudos [?]: 34 [0], given: 0

Re: Std Deviation [#permalink]  22 Dec 2005, 21:10
none...................

less than 440, group a = 68%/2 = 34%
less than 440, group b = 5%/2 = 2.5%

req % = 2.5%/36.5% = 1/14.6
Manager
Joined: 13 Dec 2005
Posts: 64
Followers: 1

Kudos [?]: 3 [0], given: 0

Std Deviation [#permalink]  22 Dec 2005, 21:13
Thanks for your response...however I have no idea how you calculated this. Further...I'm not even really sure what a standard deviation is other than knowing it has something to do with the distance from the mean. From reading the princeton review...I thought we wouldn't ever deal with these types of problems unless it was "how many std deviations away from this number is that number".
VP
Joined: 06 Jun 2004
Posts: 1061
Location: CA
Followers: 2

Kudos [?]: 36 [0], given: 0

[#permalink]  22 Dec 2005, 23:04
Two different groups of test-takers received scores on the GXYZ standardized test. Group A's scores had a normal distribution with a mean of 460 and a standard deviation of 20. Group B's scores had a normal distribution with a mean of 520 and a standard deviation of 40. If each group has the same number of test-takers, what fraction of the test-takers who scored below 440 belonged to Group B?

Answer is A

Assuming there are 100 people who took test A and 100 people who took test B.

Group A: 440 is 1 SD away from the mean, therefore, approx 16 ppl scored below 440 (Between 1 SD and the mean, percentage is roughly 34%)

Group B: 440 is 2 SDs away from the mean, therefore, approx 2 ppl scored below 440.

2/(16+2) = 2/18 ==> 1/9

Note: For a normal bell-curve distribution, between the mean and 1 SD, the percentage is approx 34%. Between 1 SD and 2 SD, approx 13.6%. Between 2 SD and on....approx 2%
_________________

Don't be afraid to take a flying leap of faith.. If you risk nothing, than you gain nothing...

Last edited by TeHCM on 23 Dec 2005, 22:20, edited 1 time in total.
Manager
Joined: 13 Dec 2005
Posts: 64
Followers: 1

Kudos [?]: 3 [0], given: 0

Std Deviation [#permalink]  23 Dec 2005, 05:40
Quote:
Note: Between the mean and 1 SD, the percentage is approx 34%. Between 1 SD and 2 SD, approx 13.6%. Between 2 SD and on....approx 2%

Does this always hold true no matter what the standard deviation?

If the mean is 750 and the standard devation is 500, will approximately 34% of the people have scores between 250 and 750?
SVP
Joined: 05 Apr 2005
Posts: 1733
Followers: 4

Kudos [?]: 34 [0], given: 0

[#permalink]  23 Dec 2005, 07:31
TeHCM wrote:
Assuming there are 100 people who took test A and 100 people who took test B.

Group A: 440 is 1 SD away from the mean, therefore, approx 16 ppl scored below 440 (Between 1 SD and the mean, percentage is roughly 34%)

Group B: 440 is 2 SDs away from the mean, therefore, approx 2 ppl scored below 440.

2/(16+2) = 2/18 ==> 1/9

Note: Between the mean and 1 SD, the percentage is approx 34%. Between 1 SD and 2 SD, approx 13.6%. Between 2 SD and on....approx 2%

goodjob...............
i was lost here. i should have take 1-.68 = .32 or 32% instead 68/2=34%. i was looking for this but.........

anyway,
less than 440, group a = 32%/2 = 16%
less than 440, group b = 5%/2 = 2.5%

req % = 2.5%/18.5 = 1/9
VP
Joined: 06 Jun 2004
Posts: 1061
Location: CA
Followers: 2

Kudos [?]: 36 [0], given: 0

Re: Std Deviation [#permalink]  23 Dec 2005, 11:44
ellisje22 wrote:
Quote:
Note: Between the mean and 1 SD, the percentage is approx 34%. Between 1 SD and 2 SD, approx 13.6%. Between 2 SD and on....approx 2%

Does this always hold true no matter what the standard deviation?

If the mean is 750 and the standard devation is 500, will approximately 34% of the people have scores between 250 and 750?

Yes this always holds true for a normal distribution.

In this case, approx 34% scored between 750 - 1,250 and 250 - 750 or 68% who scored between 250 - 1250.
_________________

Don't be afraid to take a flying leap of faith.. If you risk nothing, than you gain nothing...

Last edited by TeHCM on 23 Dec 2005, 22:58, edited 1 time in total.
Manager
Joined: 24 Oct 2005
Posts: 53
Followers: 1

Kudos [?]: 4 [0], given: 0

[#permalink]  23 Dec 2005, 17:55
Thanks TechCM, for the lucid explanation.
Manager
Joined: 12 Nov 2005
Posts: 78
Followers: 1

Kudos [?]: 5 [0], given: 0

[#permalink]  23 Dec 2005, 21:24
Thanks folks.....
I learnt a new concept in Standard Deviation today...

However I have few related questions...What are the other distributions (apart from Normal D mentioned in the question)........Does the same funda of 34%, 13.6% hold good for them as well...

Thanks in advance.
VP
Joined: 06 Jun 2004
Posts: 1061
Location: CA
Followers: 2

Kudos [?]: 36 [0], given: 0

[#permalink]  23 Dec 2005, 22:30
Kishore wrote:
Thanks folks.....
I learnt a new concept in Standard Deviation today...

However I have few related questions...What are the other distributions (apart from Normal D mentioned in the question)........Does the same funda of 34%, 13.6% hold good for them as well...

Thanks in advance.

I've edited my previous post. The 68%-98% rule only applies to a normal distribution. I think its safe to say that only normal distributions will be tested on the GMAT.

Other distributions include bimodal, multimodal, J-curve...etc. And the 68%-98% rule does not apply.
_________________

Don't be afraid to take a flying leap of faith.. If you risk nothing, than you gain nothing...

Senior Manager
Joined: 11 Nov 2005
Posts: 332
Location: London
Followers: 1

Kudos [?]: 8 [0], given: 0

[#permalink]  24 Dec 2005, 15:56
Thanx TeHCM.
It was a good tip for me.

TeHCM wrote:
Two different groups of test-takers received scores on the GXYZ standardized test. Group A's scores had a normal distribution with a mean of 460 and a standard deviation of 20. Group B's scores had a normal distribution with a mean of 520 and a standard deviation of 40. If each group has the same number of test-takers, what fraction of the test-takers who scored below 440 belonged to Group B?

Answer is A

Assuming there are 100 people who took test A and 100 people who took test B.

Group A: 440 is 1 SD away from the mean, therefore, approx 16 ppl scored below 440 (Between 1 SD and the mean, percentage is roughly 34%)

Group B: 440 is 2 SDs away from the mean, therefore, approx 2 ppl scored below 440.

2/(16+2) = 2/18 ==> 1/9

Note: For a normal bell-curve distribution, between the mean and 1 SD, the percentage is approx 34%. Between 1 SD and 2 SD, approx 13.6%. Between 2 SD and on....approx 2%
[#permalink] 24 Dec 2005, 15:56
Similar topics Replies Last post
Similar
Topics:
Two different groups of test-takers received scores on the 3 08 Dec 2007, 08:32
Two different groups of test-takers received scores on the 6 09 Jun 2007, 15:26
Two different groups of test-takers received scores on the 2 09 Nov 2006, 20:58
Two different groups of test-takers received scores on the 1 01 Nov 2006, 16:41
Two different groups of test-takers received scores on the 4 28 Nov 2005, 08:52
Display posts from previous: Sort by

# Two different groups of test-takers received scores on the

 Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group and phpBB SEO Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.