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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] New post 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] New post 12 Dec 2012, 03:26
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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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Re: A certain characteristic in a large population has a [#permalink] New post 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] New post 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
Distribution.png [ 23.16 KiB | Viewed 2896 times ]
To understand better please follow the links provided in my post above.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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] New post 13 Jan 2014, 01:28
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] New post 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
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] New post 01 Jun 2014, 04:41
Expert's post
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.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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] New post 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] New post 02 Jun 2014, 00:37
Expert's post
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.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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] 02 Jun 2014, 00:37
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