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

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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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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Nice question. Key word was symmetric to clearly mark the answer as D

OMG
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

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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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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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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You are right again. My mistake.
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experts - chetan2u, VeritasKarishma, Bunuel, nick1816, GMATBusters

When i saw this problem --- i thought to myself -- why do i need S1 or S2.

In GMAT theory, only one bell curve distribution chart is taught and in that chart, 32 % of data is ALWAYS above mean + 1 standard deviation.

I dont understand this normal vs symmetry ( i am a history major )

Are you saying we can't assume per the question stem, this is a bell curve distribution ( that is the only thing the GMAT theory teaches -- i dont see any theory on histograms or non uniform histograms for example....)

All symmetric distributions are not normal. Kurtosis is a big factor you gotta consider while making such assumption. You don't need that for GMAT tho. My point is you need either of the two statements to prove that the distribution is normal.

Yes, you cannot assume that it is a bell curve. You re given that the distribution is "symmetric". That just means it is symmetric on left and right. So mean and median lie in the centre and values lie symmetrically on their two sides. It does not necessarily mean a "normal" (bell curve) distribution. It could be a uniform distribution (all values are same). That will be symmetric too. Or some other symmetric distribution.

You NEED data from statements.
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As the distribution is asymmetric, so it's a normal distribution. The mean of the normal distribution is 50%, 34% is above the mean, then 14% is the above mean, and the rest 2% above the mean.

(1) So, 16 will be at the above m+d; Sufficient.

(2) Which means 34 is at the below mean, the other 34 above the mean and the rest 16 is at the above m+d; Sufficient.

The answer is D.
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Even though I answered it correctly, I also assumed it as normal distribution when I saw symmetric. Thank you for the detailed explanation expert people. Take away is do not assume unless and until it is explicitly stated in the question stem.

We cannot assume a normal distribution from simply reading the question stem. All we know is that we have a symmetric distribution. This only means that the left half of the distribution is a mirror image of the right half. For all we know, we can have very random but similar shapes on the two halves of the distribution.

A normal distribution is only one type of a symmetric distrubtion. It has some special properties that are listed in the two statements. Both statements are needed to conclude that we have a normal distribution.

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