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Standard deviation problem

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by jfranco23 » Mon Feb 16, 2009 5:12 pm
A certain characteristic in a large population has a distribution that is symmetric about the mean m. If 68% of the distribution lies one standard deviation d of the mean, what percent of the distribution is less than m+d?

A. 16%
B. 32%
C. 48%
D. 84%
E. 92%
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by billzhao » Mon Feb 16, 2009 5:39 pm
The answer is 84%. Am I correct?
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by jfranco23 » Mon Feb 16, 2009 5:51 pm
Yep, that is the answer, but how you get it?
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by billzhao » Mon Feb 16, 2009 6:17 pm
Refer to the graph attached.

According to the question, the shaded area (between m-d to m) + the percent between m and m+d is 68%. As the distribution is symmetric, we know that the percent betwenn m and m+d is 34%, as is shown.

Again as the distribution is symmetric, the percent on the left-hand-side of point m should be 50%.

So the percent of the distribution less than m+d is 50% + 34% = 84%

Answer is (D)
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