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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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28 Dec 2009, 11:58
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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
[Reveal] Spoiler: OA

Last edited by Bunuel on 19 Jun 2014, 05:03, 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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28 Dec 2009, 12:24
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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28 Dec 2009, 12:29
Thanks very much Shalva !!!

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

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

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28 Dec 2009, 12:29
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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

I am not familiar with deviation.

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

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

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01 Jun 2010, 05:28
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

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

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01 Jun 2010, 06:41
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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

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

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01 Jun 2010, 08:21
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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19 Jun 2014, 04:48
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Re: For a certain exam,a score of 58 was 2 standard deviations b [#permalink]

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19 Jun 2014, 05:04
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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

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.

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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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Re: For a certain exam,a score of 58 was 2 standard deviations b   [#permalink] 19 Jun 2014, 05:04
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