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by Ramit88 » Tue Jan 25, 2011 10:54 pm
f a certain sample of data has a mean of 20 and a standard deviation of 3, which of the following values is more than 2.5 standard deviations from the mean?

A. 12.0
B. 13.5
C. 17.0
D. 23.5
E. 26.5


ANS A

it says more than so should not it be 20 + 7.5 = 27.5
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by gmatmachoman » Tue Jan 25, 2011 11:18 pm
Ramit88 wrote:f a certain sample of data has a mean of 20 and a standard deviation of 3, which of the following values is more than 2.5 standard deviations from the mean?

A. 12.0
B. 13.5
C. 17.0
D. 23.5
E. 26.5


ANS A

it says more than so should not it be 20 + 7.5 = 27.5
we can divide the Normal bell cuve in terms of +3Sigma & -3 sigma.

The question asks us about teh value above 2.5 SD.

Case 1 : Mean + 2.5 *SD = 20 +7.5= 27.5.

Any value above 27.5 falls under the category of above 2.5 SD.

case 2 : Mean - 2.5 * SD : 20 - 2.5 *3 = 12.5

Any value below this 12.5 falls under the category of above 2.5SD

Here the given option satisfy case 2. Pick A
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by Anurag@Gurome » Tue Jan 25, 2011 11:23 pm
Ramit88 wrote:f a certain sample of data has a mean of 20 and a standard deviation of 3, which of the following values is more than 2.5 standard deviations from the mean?

A. 12.0
B. 13.5
C. 17.0
D. 23.5
E. 26.5

it says more than so should not it be 20 + 7.5 = 27.5
Here more than doesn't mean more in terms of numerical value but more in terms of distance.

As SD = 3 and mean = 20, 2.5*SD = 7.5.
Now any value above (20 + 7.5) = 27.5 or below (20 - 7.5) = 12.5 is more than 2.5 standard deviations from the mean.

Only such option is 12.0.

The correct answer is A.
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