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# A certain characteristic in a large population has a

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A certain characteristic in a large population has a [#permalink]

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12 Dec 2012, 03:19
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A certain characteristic in a large population has a distribution that is symmetric about the mean m. If 68 percent of the distribution lies within one standard deviation d of the mean, what percent of the distribution is less than m + d ?

(A) 16%
(B) 32%
(C) 48%
(D) 84%
(E) 92%
[Reveal] Spoiler: OA
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Re: A certain characteristic in a large population has a [#permalink]

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20 Oct 2013, 22:27
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runningguy wrote:
Not understanding this. Would someone be kind enough to provide a picture?

Thanks,
C

Check below:
Attachment:

Distribution.png [ 23.16 KiB | Viewed 17092 times ]
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Re: A certain characteristic in a large population has a [#permalink]

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12 Dec 2012, 03:26
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A certain characteristic in a large population has a distribution that is symmetric about the mean m. If 68 percent of the distribution lies within one standard deviation d of the mean, what percent of the distribution is less than m + d ?

(A) 16%
(B) 32%
(C) 48%
(D) 84%
(E) 92%

Given that 68% lies between m-d and m+d, thus 32% lies out of this range.

Now, since the distribution is symmetric about m, then half of the 32%, so 16%, lies to the right of m+d. Therefore, 16% lies to the right of m+d, and hence 84% lies to the left of m+d, which means that 84% is less than m+d.

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Hope it helps.
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Re: A certain characteristic in a large population has a [#permalink]

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13 Jan 2014, 01:28
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A certain characteristic in a large population has a distribution that is symmetric about the mean m. If 68 percent of the distribution lies within one standard deviation d of the mean, what percent of the distribution is less than m + d ?

(A) 16%
(B) 32%
(C) 48%
(D) 84%
(E) 92%

This is easiest to solve with a bell-curve histogram. m here is equal to µ in the Gaussian normal distribution and thus m = 50% of the total population.

So, if 68% is one st.Dev, then on either side of m we have 68/2 = 34%. So, 34% are to the right and left of m (= 50%). In other words, our value m + d = 50 + 34 = 84% going from the mean m, to the right of the distribution in the bell shaped histogram.. This means that 84% of the values are below m + d.

Like I said, doing it on a bell-curve histogram is much easier to fully "get" how this works, or you could apply GMAT percentile jargon/theory to it
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Re: A certain characteristic in a large population has a [#permalink]

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01 Jun 2014, 04:41
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b2bt wrote:
Bunuel wrote:
runningguy wrote:
Not understanding this. Would someone be kind enough to provide a picture?

Thanks,
C

Check below:
Attachment:
Distribution.png

-------16-------34-------m-------34-------16-------

We can't say that the 68% is divided equally on both the sides of m, can we?
I'm asking this, because that's how I solved it. However, I got it right...

You are not right. Check the diagram.

A distribution is symmetric about the mean m, implies that half of 68% is to the left of m and another half to the right of m.
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Re: A certain characteristic in a large population has a [#permalink]

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20 Oct 2013, 18:29
Not understanding this. Would someone be kind enough to provide a picture?

Thanks,
C
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Re: A certain characteristic in a large population has a [#permalink]

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01 Jun 2014, 04:18
Bunuel wrote:
runningguy wrote:
Not understanding this. Would someone be kind enough to provide a picture?

Thanks,
C

Check below:
Attachment:
Distribution.png

-------16-------34-------m-------34-------16-------

We can't say that the 68% is divided equally on both the sides of m, can we?
I'm asking this, because that's how I solved it. However, I got it right...
Current Student
Joined: 25 Sep 2012
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Re: A certain characteristic in a large population has a [#permalink]

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01 Jun 2014, 05:24
Bunuel wrote:
b2bt wrote:
-------16-------34-------m-------34-------16-------

We can't say that the 68% is divided equally on both the sides of m, can we?
I'm asking this, because that's how I solved it. However, I got it right...

You are not right. Check the diagram.

A distribution is symmetric about the mean m, implies that half of 68% is to the left of m and another half to the right of m.

Basically my doubt is
68% = m + >m-d + <m+d
OR
68% = >m-d + <m+d (and not m)

I considered the 2nd eqn and after looking at the pic I understood it that it should as the 1st eqn. Just wanted to confirm that 1st eqn is right
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Re: A certain characteristic in a large population has a [#permalink]

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02 Jun 2014, 00:37
b2bt wrote:
Bunuel wrote:
b2bt wrote:
-------16-------34-------m-------34-------16-------

We can't say that the 68% is divided equally on both the sides of m, can we?
I'm asking this, because that's how I solved it. However, I got it right...

You are not right. Check the diagram.

A distribution is symmetric about the mean m, implies that half of 68% is to the left of m and another half to the right of m.

Basically my doubt is
68% = m + >m-d + <m+d
OR
68% = >m-d + <m+d (and not m)

I considered the 2nd eqn and after looking at the pic I understood it that it should as the 1st eqn. Just wanted to confirm that 1st eqn is right

I don't understand what you mean by either of the above equations.
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Re: A certain characteristic in a large population has a [#permalink]

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10 Jun 2015, 04:54
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Re: A certain characteristic in a large population has a [#permalink]

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04 Jul 2016, 02:35
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20 Jul 2016, 10:55
A certain characteristic in a large population has a distribution that is symmetric about the mean m. If 68% of the distribution lies within one standard deviation d of the mean, what percent of the distribution is less than m+d?

A. 16%
B. 32%
C. 48%
D. 84%
E. 92%
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Re: A certain characteristic in a large population has a [#permalink]

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20 Jul 2016, 11:08
Saayan wrote:
A certain characteristic in a large population has a distribution that is symmetric about the mean m. If 68% of the distribution lies within one standard deviation d of the mean, what percent of the distribution is less than m+d?

A. 16%
B. 32%
C. 48%
D. 84%
E. 92%

Merging topics.

Please refer to the discussion above.

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A certain characteristic in a large population has a [#permalink]

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23 Jul 2016, 02:03
A certain characteristic in a large population has a distribution that is symmetric about the mean m. If 68 percent of the distribution lies within one standard deviation d of the mean, what percent of the distribution is less than m + d ?

(A) 16%
(B) 32%
(C) 48%
(D) 84%
(E) 92%

Any large population has a characteristic graph known as the Normal distribution curve that looks like a bell.
SEE THE ATTACHED IMAGE
The unique property of Normal distribution is that 68% of samples lies with in the 1st SD. 95% of samples fall with in 2nd SD and about 99% of samples fall within the 3rd sd.
The Normal distraction curve is symmetric around the arithmetic mean and positive SD and negative SD are equidistant from the mean
Half of the samples lies on the left of the mean and half of the samples lies on the right on the mean.
The x axis has the following form
3SD...........2SD.........MEAN...........2SD............3SD
3d.............2d..........mean............d................3d
2%............14%<---------50%---------->84%..............99%
m+d=84%
therefore remaining samples = 100-84 = 16

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A certain characteristic in a large population has a   [#permalink] 23 Jul 2016, 02:03
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