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by grandh01 » Fri Jul 06, 2012 10:09 am
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 is the mean score for the examination.

1) 74
2) 76
3) 78
4) 80
5)82

OA is A

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by tutorphd » Fri Jul 06, 2012 10:24 am
m = mean
sig = standard deviation

translate the information into equations:

58 = m - 2*sig
98 = m + 3*sig

Solve the system for m: m=74

This problem is more about solving a system of two equations with two unknowns than about statistics. The statistics terms are just red herring to scare you away :)
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by GMATGuruNY » Fri Jul 06, 2012 12:40 pm
grandh01 wrote: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 is the mean score for the examination.

1) 74
2) 76
3) 78
4) 80
5)82
58<---d---><---d--->mean<---d---><---d---><---d--->98.

As the figure above shows, there are a total of 5 standard deviations between 58 and 98.
Thus, d = (98-58)/5 = 8.
Since 58 is 2 standard deviations BELOW the mean, the mean = 58+d+d = 58+8+8 = 74.

The correct answer is A.
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