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The heights of boys in a schools are normally distributed. B

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KomalSg
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The heights of boys in a schools are normally distributed. B [#permalink] New post   07 May 2020, 23:56
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The heights of boys in a school are normally distributed. Boy1's height is at 80th percentile. Boy2's height is at 20th percentile.

Quantity A
Quantity B
Percentage of students whose heights are less than or equal to Boy 1's height
Percentage of students whose height are more than Boy 2's height.


A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
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A
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Re: The heights of boys in a schools are normally distributed. B [#permalink] New post   09 May 2020, 06:05
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KomalSg wrote:
The heights of boys in a school are normally distributed. Boy1's height is at 80th percentile. Boy2's height is at 20th percentile.

Quantity A
Quantity B
Percentage of students whose heights are less than or equal to Boy 1's height
Percentage of students whose height are more than Boy 2's height.


A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.


Would the answer be C or A?


Let's say there are 100 students in the school.

If Boy 1's height is in the 80th percentile, then if we arrange all of the heights in ascending order, Boy 1's height will be the 81st value.
Since 80 heights are less than Boy 1's height, this means Boy 1's height is in the 80th percentile.

If Boy 2's height is in the 20th percentile, then if we arrange all of the heights in ascending order, Boy 2's height will be the 21st value.
Since 20 heights are less than Boy 2's height, this means Boy 2's height is in the 20th percentile.

Quantity A: Percentage of students whose heights are less than OR EQUAL TO Boy 1's height
If we arrange all of the heights in ascending order, Boy 1's height will be the 81st value, which means there are 81 students whose heights are less than or equal to Boy 1's height.
In other words, 81 percent of students have heights that are less than or equal to Boy 1's height.

Quantity B: Percentage of students whose height are more than Boy 2's height.
Important: Quantity A featured the words "or equal to," whereas Quantity B does not have those same words.
If we arrange all of the heights in ascending order, Boy 2's height will be the 21st value.
100 - 21 = 79. So, there are 79 students whose heights are greater than Boy 2's height.
In other words, 79 percent of students have heights that are greater than Boy 2's height.

Answer: A

Cheers,
Brent
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Re: The heights of boys in a schools are normally distributed. B [#permalink] New post   09 May 2020, 02:44
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Re: The heights of boys in a schools are normally distributed. B [#permalink] New post   09 May 2020, 03:53
Is it the kind of percentile math? I think the answer would be C.
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Re: The heights of boys in a schools are normally distributed. B [#permalink] New post   12 May 2020, 11:41
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Here, the trap is in the wording of the question. In quantity A they mention 'equal to or less than' while in quantity B they mention 'more than' (not including the 20th percentile). So choice A>B. if the quantity B said more than or equal to then the answer would have been choice C.
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Re: The heights of boys in a schools are normally distributed. B [#permalink] New post   18 Aug 2022, 00:13
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safana wrote:
Here, the trap is in the wording of the question. In quantity A they mention 'equal to or less than' while in quantity B they mention 'more than' (not including the 20th percentile). So choice A>B. if the quantity B said more than or equal to then the answer would have been choice C.


if Quantity B mentions 'greater than or equal to', shouldn't the answer be 'D' ?
Since,
(i) it is not mentioned that all boys have distinct heights
and
(ii) we also do not know how many boys have the same height as either Boy1 or Boy2

Please Help!

Thank you.
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Re: The heights of boys in a schools are normally distributed. B [#permalink] New post   22 Oct 2022, 13:34
GreenlightTestPrep wrote:
KomalSg wrote:
The heights of boys in a school are normally distributed. Boy1's height is at 80th percentile. Boy2's height is at 20th percentile.

Quantity A
Quantity B
Percentage of students whose heights are less than or equal to Boy 1's height
Percentage of students whose height are more than Boy 2's height.


A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.


Would the answer be C or A?


Let's say there are 100 students in the school.

If Boy 1's height is in the 80th percentile, then if we arrange all of the heights in ascending order, Boy 1's height will be the 81st value.
Since 80 heights are less than Boy 1's height, this means Boy 1's height is in the 80th percentile.

If Boy 2's height is in the 20th percentile, then if we arrange all of the heights in ascending order, Boy 2's height will be the 21st value.
Since 20 heights are less than Boy 2's height, this means Boy 2's height is in the 20th percentile.

Quantity A: Percentage of students whose heights are less than OR EQUAL TO Boy 1's height
If we arrange all of the heights in ascending order, Boy 1's height will be the 81st value, which means there are 81 students whose heights are less than or equal to Boy 1's height.
In other words, 81 percent of students have heights that are less than or equal to Boy 1's height.

Quantity B: Percentage of students whose height are more than Boy 2's height.
Important: Quantity A featured the words "or equal to," whereas Quantity B does not have those same words.
If we arrange all of the heights in ascending order, Boy 2's height will be the 21st value.
100 - 21 = 79. So, there are 79 students whose heights are greater than Boy 2's height.
In other words, 79 percent of students have heights that are greater than Boy 2's height.

Answer: A

Cheers,
Brent


Sorry if it is a repeating question, but it is something that always confuses me.
If there are 100 students. Why the 80th percentile student is the 81 student and not the 80 student?
I assume it is because of the even/odd area, but maybe you can explain it in a better way?
Thanks!
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Re: The heights of boys in a schools are normally distributed. B [#permalink] New post   10 Nov 2023, 02:50
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