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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%
[Reveal] Spoiler: OA
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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%


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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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, 05:41
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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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Re: A certain characteristic in a large population has a [#permalink]

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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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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, 06:24
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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New post 02 Jun 2014, 01:37
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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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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

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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

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

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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
Re: A certain characteristic in a large population has a   [#permalink] 01 May 2017, 20:58
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