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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
OA A
For a certain exam, a score of 58 was 2 standard deviations
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If we let x = mean and s = standard deviation, then a score of 58 that was 2 standard deviations below the mean would mean 58 = x - 2s. Similarly, a score of 98 that was 3 standard deviations above the mean would mean 98 = x + 3s.AAPL wrote:GMAT Prep
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
OA A
We can use the two equations to determine a value of x.
x - 2s = 58
x + 3s = 98
If we subtract the first equation from the second equation, we have:
5s = 40
s = 8
Now we can determine x:
x + 3s = 98
x + 3(8) = 98
x + 24 = 98
x = 74
Answer: A
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