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Standard deviation

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Standard deviation

by NehaPathak » Fri Sep 23, 2011 1:20 pm
The lifetime of all the batteries produced by a certain company in a year have a distribution that is symmetric about the mean "m". If the distribution has the standard deviatin "d", what percent of the distribution greater than m+d?

1)68% of the distribution lies in the interval from m-d to m+d, inclusive
2)16% of the distribution less than than m-d.
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by cans » Fri Sep 23, 2011 7:52 pm
m,d

B) 16% less than m-d. as symmetrical wrt to m, thus 16% greater then m+d sufficient

A) 68% in interval. thus 32% outside interval. thus 16% greater than m+d (symmetry)
IMO D
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by navami » Mon Sep 26, 2011 1:07 am
IMO D too
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by Anurag@Gurome » Mon Sep 26, 2011 5:14 am
NehaPathak wrote:The lifetime of all the batteries produced by a certain company in a year have a distribution that is symmetric about the mean "m". If the distribution has the standard deviatin "d", what percent of the distribution greater than m+d?

1)68% of the distribution lies in the interval from m-d to m+d, inclusive
2)16% of the distribution less than than m-d.
If the distribution is symmetric about the mean then it means that 50% of the population is above and below the mean.

(1) 68% of the distribution lies in the interval from m-d to m+d implies that 34% is either above or below the mean. Out of 100, 32% population is outside 1 SD of the mean so 16% of the population is m + d and 16% as m - d; SUFFICIENT.

(2) 16% of the distribution less than than m - d is again the same as the info given in statement 1; SUFFICIENT.

The correct answer is D.
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