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The lifetime of all the batteries produced by a certain company in a

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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

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Originally posted by vigneshpandi on 21 Sep 2010, 21:34.
Last edited by Bunuel on 03 Jan 2019, 03:53, edited 2 times in total.
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New post 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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New post 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.
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Re: The lifetime of all the batteries produced by a certain company in a  [#permalink]

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New post 22 Sep 2010, 16:42
Nice question. Key word was symmetric to clearly mark the answer as D
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Re: The lifetime of all the batteries produced by a certain company in a  [#permalink]

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New post 16 Mar 2011, 00:31
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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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Re: The lifetime of all the batteries produced by a certain company in a  [#permalink]

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New post 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: The lifetime of all the batteries produced by a certain company in a  [#permalink]

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New post 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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New post 02 Jul 2013, 06:57
Bunuel 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 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.


How valuable is the portion in red if you don't read the question carefully would have marked C instead of D!
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Re: The lifetime of all the batteries produced by a certain company in a  [#permalink]

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New post 15 Jul 2016, 10:17
vigneshpandi 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 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...


The answer is D

Statement 1) (1) 68 percent of the distribution lies in the interval from m-d to m+d, inclusive
Standard deviation is a bell curve with m at the centre and +d on the right and -d not the left. (But remember standard deviation in itself can never be negative)
Also remember the graph of Standard deviation is the most symmetric graph that you will see in mathematics. It also has some unique properties related to (mean + deviation) and (mean + 2 * deviation) and so on
but for this question this much info is enough.
Therefore if you assume m to be at point 0 then m+d=34% and m-d= 34 %
we want to know the value of m+d ; SUFFICIENT

2) 16 percent of the distribution is less than m-d
Since 16 % of distribution is less than m-d therefore 16 % of the distribution will be more than m+d ; a totalof 32% of 100 leaving 68% to be distributed equally into
m+d and m-d
therefore both m+d and m-d will be 68/2 = 34
Sufficient

Answer is D
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Re: The lifetime of all the batteries produced by a certain company in a  [#permalink]

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New post 10 Feb 2017, 10:40
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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New post 13 Sep 2017, 19:17
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Bunuel anairamitch1804

Is not statement 1 a std rule for all normal distribution curve / bell curve?
Please refer attachment.

Thanks in advance.
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New post 02 Jan 2019, 20:42
adkikani wrote:
Bunuel anairamitch1804

Is not statement 1 a std rule for all normal distribution curve / bell curve?
Please refer attachment.

Thanks in advance.



You are right. In fact, we do not need either statement to answer the question. 68 % is always within 1 SD.
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New post 03 Jan 2019, 04:00
cledgard wrote:
adkikani wrote:
Bunuel anairamitch1804

Is not statement 1 a std rule for all normal distribution curve / bell curve?
Please refer attachment.

Thanks in advance.



You are right. In fact, we do not need either statement to answer the question. 68 % is always within 1 SD.


We are not told that we have a "normal distribution", we are told that we have a symmetric distribution. Not all symmetric distributions are normal distributions.
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Re: The lifetime of all the batteries produced by a certain company in a  [#permalink]

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New post 03 Jan 2019, 18:08
Bunuel wrote:
cledgard wrote:
adkikani wrote:
Bunuel anairamitch1804

Is not statement 1 a std rule for all normal distribution curve / bell curve?
Please refer attachment.

Thanks in advance.



You are right. In fact, we do not need either statement to answer the question. 68 % is always within 1 SD.


We are not told that we have a "normal distribution", we are told that we have a symmetric distribution. Not all symmetric distributions are normal distributions.


You are right again. My mistake.
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