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For a certain exam,a score of 58 was 2 standard deviations b

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For a certain exam,a score of 58 was 2 standard deviations b  [#permalink]

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New post Updated on: 19 Jun 2014, 04:03
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For a certain exam,a score of 58 was 2 standard deviations below mean and a score of 98 was 3 standard deviations above mean.What was the mean score for the exam?

A. 74
B. 76
C. 78
D. 80
E. 82

OPEN DISCUSSION OF THIS QUESTION IS HERE: for-a-certain-exam-a-score-of-58-was-2-standard-deviations-b-128661.html

Originally posted by nailgmattoefl on 28 Dec 2009, 10:58.
Last edited by Bunuel on 19 Jun 2014, 04:03, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
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Re: For a certain exam,a score of 58 was 2 standard deviations b  [#permalink]

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New post 28 Dec 2009, 11:24
2
Definition and properties of StDev are not crucial for this problem.

let's denote deviation with \(x\)

Quote:
a score of 58 was 2 standard deviations below the mean

\(58=mean-2x\)


Quote:
a score of 98 was 3 standard deviations above the mean

\(98=mean+3x\)

We have 2 equations and 2 variables. So this linear system of equations can be solved. let's just subtract Statement1 from Statement 2:
\(98-58=mean +3x-mean+2x\)
\(40=5x\)
\(x=8\)
\(mean=98-3x=98-24=74\)
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Re: For a certain exam,a score of 58 was 2 standard deviations b  [#permalink]

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New post 28 Dec 2009, 11:29
Thanks very much Shalva !!!

Indeed with the definition of Mean, the problem is solving by himself.

I need to review some maths concepts :-D
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Re: For a certain exam,a score of 58 was 2 standard deviations b  [#permalink]

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New post 28 Dec 2009, 11:29
nailgmattoefl wrote:
Hello,

Here is the statement:

"For a certain examination, a score of 58 was 2 standard deviations below the mean, and a score of 98 was 3 standard deviations above the mean, what was the mean score for the examination?"
Choices: 74, 76, 80, 82
Correct answer: 74

I am not familiar with deviation.

Thanks in advance


A score of 58 was 2 standard deviations below the mean --> 58=Mean-2d
A score of 98 was 3 standard deviations above the mean --> 98=Mean+3d

Solving above for Mean=74

For more about the Standard Deviation please check: Standard Deviation.
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Re: For a certain exam,a score of 58 was 2 standard deviations b  [#permalink]

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New post 01 Jun 2010, 04:28
Can anyone help me with this problem please? It comes from the Gmat Testprep.

For a certain examination, a score of 58 was 2 standard deviations below the mean, and a score of 98 was 3 standard deviations above the mean. What was the mean score for the examination?

A. 74
B. 76
C. 78
D. 80
E. 82

The right answer is A.
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Re: For a certain exam,a score of 58 was 2 standard deviations b  [#permalink]

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New post 01 Jun 2010, 05:41
2
1
Let \(d\) stand for Standard Deviation, \(M\) - for mean. We can construct a system of equations:

\(\begin{cases} M - 2d = 58 \\ M + 3d = 98 \end{cases}\)

After you subtract the first equation from the second, you get this equation:

\(5d = 40\)
\(d = 8\)

After plugging the value of \(d\) in the first equation, you get the value of \(M\):

\(M = 58 + 2*8 = 74\)

I hope it helps you.
jessicavanessa wrote:
Can anyone help me with this problem please? It comes from the Gmat Testprep.

For a certain examination, a score of 58 was 2 standard deviations below the mean, and a score of 98 was 3 standard deviations above the mean. What was the mean score for the examination?

A. 74
B. 76
C. 78
D. 80
E. 82

The right answer is A.

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Re: For a certain exam,a score of 58 was 2 standard deviations b  [#permalink]

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New post 01 Jun 2010, 07:21
Thank you !
Very useful
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Re: For a certain exam,a score of 58 was 2 standard deviations b  [#permalink]

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New post 19 Jun 2014, 04:04
For a certain exam,a score of 58 was 2 standard deviations below mean and a score of 98 was 3 standard deviations above mean.What was the mean score for the exam?

A. 74
B. 76
C. 78
D. 80
E. 82

A score of 58 was 2 standard deviations below the mean --> 58 = Mean - 2d
A score of 98 was 3 standard deviations above the mean --> 98 = Mean + 3d

Solving above for Mean = 74.

Answer: A.

For more about the Standard Deviation please check: Standard Deviation.

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OPEN DISCUSSION OF THIS QUESTION IS HERE: for-a-certain-exam-a-score-of-58-was-2-standard-deviations-b-128661.html
_________________

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Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: For a certain exam,a score of 58 was 2 standard deviations b  [#permalink]

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