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# Standard deviation problem

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Senior Manager
Joined: 08 Jan 2009
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Standard deviation problem [#permalink]  31 Jul 2009, 19:08
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Difficulty:

(N/A)

Question Stats:

75% (01:10) correct 25% (01:04) wrong based on 3 sessions
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%

[Reveal] Spoiler:
Ans D
Senior Manager
Joined: 08 Jan 2009
Posts: 329
Followers: 2

Kudos [?]: 93 [0], given: 5

Re: Standard deviation problem [#permalink]  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%
Senior Manager
Joined: 25 Jun 2009
Posts: 308
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Kudos [?]: 93 [0], given: 6

Re: Standard deviation problem [#permalink]  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: 170
Location: India
Schools: South Asian B-schools
Followers: 2

Kudos [?]: 68 [1] , given: 37

Re: Standard deviation problem [#permalink]  07 Aug 2009, 06:27
1
KUDOS
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 %
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Manager
Joined: 10 Jul 2009
Posts: 129
Location: Ukraine, Kyiv
Followers: 2

Kudos [?]: 72 [0], given: 60

Re: Standard deviation problem [#permalink]  16 Sep 2009, 07:23
Try wikipedia to make it clear.

http://en.wikipedia.org/wiki/Normal_distribution
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Manager
Joined: 27 Oct 2008
Posts: 185
Followers: 1

Kudos [?]: 116 [0], given: 3

Re: Standard deviation problem [#permalink]  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
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Re: Standard deviation problem [#permalink]  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%
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Re: Standard deviation problem   [#permalink] 17 May 2011, 23:28
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