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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, 10:58

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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?

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

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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: \(98-58=mean +3x-mean+2x\) \(40=5x\) \(x=8\) \(mean=98-3x=98-24=74\)

"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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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]

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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]

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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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