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For a certain exam,a score of 58 was 2 standard deviations b [#permalink]
28 Dec 2009, 10:58
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81% (01:45) correct
19% (01:07) wrong based on 122 sessions
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?
Re: For a certain exam,a score of 58 was 2 standard deviations b [#permalink]
28 Dec 2009, 11:24
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: \(98-58=mean +3x-mean+2x\) \(40=5x\) \(x=8\) \(mean=98-3x=98-24=74\)
Re: For a certain exam,a score of 58 was 2 standard deviations b [#permalink]
28 Dec 2009, 11:29
Expert's post
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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 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. _________________
Re: For a certain exam,a score of 58 was 2 standard deviations b [#permalink]
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?
Re: For a certain exam,a score of 58 was 2 standard deviations b [#permalink]
01 Jun 2010, 05:41
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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?
Re: For a certain exam,a score of 58 was 2 standard deviations b [#permalink]
19 Jun 2014, 03:48
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Re: For a certain exam,a score of 58 was 2 standard deviations b [#permalink]
19 Jun 2014, 04:04
Expert's post
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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
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