The lifetime of all the batteries produced by a certain comp

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The lifetime of all the batteries produced by a certain comp [#permalink]

21 Sep 2010, 21:34

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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 a standard deviation of d, what percent of the distribution is greater than m+d?

(1) 68 percent of the distribution lies in the interval from m-d to m+d, inclusive
(2) 16 percent of the distribution is less than m-d

Can sum1 explain the concept behind this...Looking at the answer I have come up with my own assumptions...

[Reveal] Spoiler: OA

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Last edited by Bunuel on 02 Feb 2012, 10:48, edited 1 time in total.

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Re: SD symmetric about the mean [#permalink]

21 Sep 2010, 21:59

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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 a standard deviation of d, what percent of the distribution is greater than m+d?

Symmetric about the mean means that the shape of the distribution on the right and left side of the curve are mirror-images of each other.

(1) 68% of the distribution lies in the interval from m-d to m+d, inclusive --> 100%-68%=32% is less than m-d and more than m+d. As distribution is symmetric about the mean then exactly half of 32%, or 16%, would be more than m+d. Sufficient.

(2) 16% of the distribution is less than m-d --> again, as distribution is symmetric about the mean then exactly 16%, will be more than m+d. Sufficient.

Answer: D.

Hope it helps.
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Re: SD symmetric about the mean [#permalink]

22 Sep 2010, 16:34

Thank you. I drew a diagram with normal distribution and came up with this assumptions...But now I am happy looking at ur explanations that my assumptions are true.
+1
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Re: SD symmetric about the mean [#permalink]

22 Sep 2010, 16:42

Nice question. Key word was symmetric to clearly mark the answer as D
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Re: SD symmetric about the mean [#permalink]

16 Mar 2011, 00:31

Bunuel wrote:

The lifetime of all the batteries produced by certain companies have a distribution which is symmetric about mean m. If the distribution has a standard deviation of d , what percentage of distribution is greater than m+d?

Symmetric about the mean means that the shape of the distribution on the right and left side of the curve are mirror-images of each other.

(1) 68% of the distribution lies in the interval from m-d to m+d, inclusive --> 100%-68%=32% is less than m-d and more than m+d. As distribution is symmetric about the mean then exactly half of 32%, or 16%, would be more than m+d. Sufficient.

(2) 16% of the distribution is less than m-d --> again, as distribution is symmetric about the mean then exactly 16%, will be more than m+d. Sufficient.

Answer: D.

Hope it helps.

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You make all these horible definitions easier to breathe. i used to be of much fear when thinking of DS but when looking some explanations here, i feel the world is not so dark :oops:

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Re: SD symmetric about the mean [#permalink]

16 Mar 2011, 22:49

This is all related to the concepts related to bell curve and normal distribution.

Bunuel/Ian, are these concepts tested in GMAT ?
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Re: SD symmetric about the mean [#permalink]

02 Feb 2012, 10:09

@ ghosh

bell curve is an important topic and often questions crop up.
i got one such in my gmat, though it was east, but the qs stem is verbose and one has to make out that its a qs on bell curve.
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Re: SD symmetric about the mean [#permalink] 02 Feb 2012, 10:09

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