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by teejaycrown » Sat Oct 20, 2012 11:58 am
For a certain examination, a score of 58 was 2 standard deviation below the mean, and a score of 98 was 3 standard deviation above the mean. What was the mean score for the examination
74, 76, 78, 80, 82.
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by Brent@GMATPrepNow » Sat Oct 20, 2012 12:03 pm
teejaycrown wrote:For a certain examination, a score of 58 was 2 standard deviation below the mean, and a score of 98 was 3 standard deviation above the mean. What was the mean score for the examination
74, 76, 78, 80, 82.
Typically, the GMAT uses the term "units of standard deviation"
So, if the SD is 4, then 1 unit of SD = 4
Similarly, 2 units of SD = 8
And 1.5 units of SD = 6
If the mean is 10 and the SD is 4, then we say that 18 is 2 units of SD above the mean since 10 + 2(4) = 18
Similarly, we say that 6 is 1 unit of SD below the mean since 10 - 4 = 4

For your question, we can let M=mean and let D=the standard deviation
So, 58 is 2 standard deviations below the mean translates into M - 2D = 58
and 98 is 3 standard deviations above the mean translates into M + 3D = 98

When we solve this system of equations, we get M=74 and D=8

So the answer is A

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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