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# The mean score in a certain test is 80. If the test scores have a norm

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Manager
Joined: 08 Jan 2009
Posts: 202
The mean score in a certain test is 80. If the test scores have a norm  [#permalink]

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31 Jul 2009, 19:08
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Difficulty:

55% (hard)

Question Stats:

53% (01:31) correct 47% (01:23) wrong based on 103 sessions

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The mean score in a certain test is 80. If the test scores have a normal distribution and the standarad distribution is 7, what percent of examinees score between 66 and 94?

A) 50%
B) 68%
C) 82%
D) 96%
E) 98%
Manager
Joined: 08 Jan 2009
Posts: 202
Re: The mean score in a certain test is 80. If the test scores have a norm  [#permalink]

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02 Aug 2009, 19:30
Thank you.

I read through the description now i get it.

The percentages 34: 14 : 2 corresponds to the 1st , 2nd and 3rd standard deviation on each side of the mean.

So our case 66 and 94 are two std deviation away from the mean.

14 + 34 + 34 + 14 = 96%
Manager
Joined: 25 Jun 2009
Posts: 211
Re: The mean score in a certain test is 80. If the test scores have a norm  [#permalink]

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02 Aug 2009, 21:41
tkarthi4u wrote:
Thank you.

I read through the description now i get it.

The percentages 34: 14 : 2 corresponds to the 1st , 2nd and 3rd standard deviation on each side of the mean.

So our case 66 and 94 are two std deviation away from the mean.

14 + 34 + 34 + 14 = 96%

Hi,
Can you please explain how did you get that?

Thanks
Manager
Joined: 18 Jul 2009
Posts: 123
Location: India
Schools: South Asian B-schools
Re: The mean score in a certain test is 80. If the test scores have a norm  [#permalink]

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07 Aug 2009, 06:27
2
1
Normal distribution says

1 sigma = 68% (34% on either side) population
2 sigma = 96% (14% on either side) population so 68% +14%x 2=96%
3 sigma = 99.99% (2% on either side) population so 96% + 2% x 2 ~ 99.99 %
Manager
Joined: 10 Jul 2009
Posts: 83
Location: Ukraine, Kyiv
Re: The mean score in a certain test is 80. If the test scores have a norm  [#permalink]

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16 Sep 2009, 07:23
Try wikipedia to make it clear.

http://en.wikipedia.org/wiki/Normal_distribution
Manager
Joined: 27 Oct 2008
Posts: 128
Re: The mean score in a certain test is 80. If the test scores have a norm  [#permalink]

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19 Sep 2009, 06:06
The mean score in a certain test is 80. If the test scores have a normal distribution and the standarad distribution is 7, what percent of examinees score between 66 and 94?

A) 50%
B) 68%
C)82%
D)96%
E)98%

Soln: Here mean = 80
and standard deviation sig = 7
Since for a range of scores from 66 to 94, the scores vary between 2 * sig about mean
that is from -2 * sig to +2 * sig
for this range with normal distribution the percent of examinees is
= 13.6 + 34.1 + 34.1 + 13.6
= 95.4
Approximately 96%
Ans is D
Director
Status: There is always something new !!
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Joined: 08 May 2009
Posts: 723
Re: The mean score in a certain test is 80. If the test scores have a norm  [#permalink]

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17 May 2011, 23:28
interesting concept.

73 - 80 and 80-87 = 1 sigma = 34*2

66-73 and 87- 94 = 2 sigma = 14 * 2

total 96%
Manager
Joined: 20 Apr 2014
Posts: 87
Re: The mean score in a certain test is 80. If the test scores have a norm  [#permalink]

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24 Sep 2015, 01:25
i need more explanation from experts please. will I see this type of Qs in Gmat Test ?
Manager
Joined: 23 Sep 2015
Posts: 79
Concentration: General Management, Finance
GMAT 1: 680 Q46 V38
GMAT 2: 690 Q47 V38
GPA: 3.5
Re: The mean score in a certain test is 80. If the test scores have a norm  [#permalink]

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07 Nov 2015, 21:41
1
This question is just testing standard knowledge of a normal distribution graph.

The mean=80, mean 50% of the data falls above and below this point,

When we consider 1 standard deviation on either side of it, we are cutting the data points of interest down to 34% on each side, or 68% between them

As for the question we are being asked about the range +/- 2 SD from the mean. This tests us just knowing that this represents 96% of the data of the data points, or 48% on either side of the mean.

Hope this helps someone
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Joined: 17 Jul 2014
Posts: 2435
Location: United States (IL)
Concentration: Finance, Economics
GMAT 1: 650 Q49 V30
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WE: General Management (Transportation)
Re: The mean score in a certain test is 80. If the test scores have a norm  [#permalink]

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28 Nov 2015, 09:31
normal distribution represents the bell curve, in which 50% is above mean, and 50% below mean
34% lies within 1 standard deviation or mean+SD and mean-SD
mean+-SD is 73 and 87.
68% of people have scores between 73 and 87
now, aprox. 14% is between (mean+2SD)-(Mean+SD), this is the same for mean minus 2 SD.
Mean+2SD=94
Mean-2SD=66

ok, so in total, we have 68% + 28 = aprox. 98%.
Re: The mean score in a certain test is 80. If the test scores have a norm   [#permalink] 28 Nov 2015, 09:31

# The mean score in a certain test is 80. If the test scores have a norm

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