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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 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%
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Walkabout wrote:
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.

Answer: D.

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Hope it helps.
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Not understanding this. Would someone be kind enough to provide a picture?

Thanks,
C

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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
Distribution.png [ 23.16 KiB | Viewed 25089 times ]
To understand better please follow the links provided in my post above.
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Re: A certain characteristic in a large population has a [#permalink]

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Walkabout wrote:
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 :-D

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

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New post 01 Jun 2014, 05:18
Bunuel wrote:
runningguy wrote:
Not understanding this. Would someone be kind enough to provide a picture?

Thanks,
C


Check below:
Attachment:
Distribution.png
To understand better please follow the links provided in my post above.


-------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...

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

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New post 01 Jun 2014, 05:41
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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
To understand better please follow the links provided in my post above.


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

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New post 23 Jul 2016, 03:03
Walkabout wrote:
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

ANSWER IS A

Image
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New post 25 Mar 2017, 06:42
question says that 68% of population lies within 1 standard deviation, so this means that (Mean+deviation)-(Mean-deviation|=68%
the rest is 32. 16 to the very left, 16 to the very right. We need to find from the very left to the m+d, this is 16+68=84

Answer is D

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

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New post 22 Apr 2017, 13:19
Hi... Can you tell me how do you know that (m-d)<68%<(m+d)
i didnt get the logic.. Please help...

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

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New post 01 May 2017, 15:10
Drawing a bell curve such as the one in Bunuel's diagram makes this question a lot easier to visualize.

68% of the population lies within one std dev of the mean (one std dev above and one std dev below the mean). This tells us that 32% of the population is outside of this range, or 16% on either side of the one std devs each way. Hence, the portion under m+d equals 68% + 16% = 84%.

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

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New post 01 May 2017, 20:58
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%

symmetric about mean that is 50% left and 50% right so less than m+d is 68+16=84

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

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New post 01 Aug 2017, 01:29
This is how much i understood from the question, Since a bell shaped curve is symmetric and the 68% of the population is within 1 standard deviation of the mean then 68/2 =34% of the population is m+d and 34% of the population is m-d, Also the rest 32%(100-68) which is 16% for m-2d and m-3d , Therefore 34+16=50% is less than m+d. After this is what I am not understanding. Can someone please explain? U Thank you in advance.

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

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New post 10 Oct 2017, 10:32
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Walkabout wrote:
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%


Let's first sketch a distribution that is symmetric about the mean m.
Image
Notice that m+d represents 1 unit of standard deviation ABOVE the mean
Likewise, m-d represents 1 unit of standard deviation BELOW the mean
And m+2d represents 2 units of standard deviation ABOVE the mean, etc.
ASIDE: There are infinitely many distributions that are symmetric about the mean m. The above distribution is just one.

Our goal is to determine what portion of the population is LESS THAN than m+d
Image

First recognize that, since the distribution is symmetric about the mean m, 50% of the population is BELOW the mean, and 50% is ABOVE the mean.
Image

Next, we're told that 68% of the distribution lies within one standard deviation d of the mean
In other words, 68% the population is BETWEEN m-d and m+d
Image

Since the distribution is symmetric about the mean m, this 68%, is divided into two equal populations.
Image

When we COMBINE our two findings, we see that the percentage of the population that's below m+d = 50% + 34% = 84%
Image

Answer:
[Reveal] Spoiler:
D


Cheers,
Brent
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Re: A certain characteristic in a large population has a   [#permalink] 10 Oct 2017, 10:32
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