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The random variable X is normally distributed.

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The random variable X is normally distributed. [#permalink] New post 09 Feb 2018, 04:58
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85% (00:47) correct 14% (01:40) wrong based on 7 sessions
Hey guys, I just stumbled across a question in the 2nd edition guide of which I think the official answer is wrong.
Please help me out on this one:

The random variable X is normally distributed. The values 650 and 850 are the 60th and 90th percentiles of the distribution of X, respectively.

Quantity A
Quantity B
The value at the 75th percentile of the distribution of X
750




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



I'd say the answer is D, however in the official answers they say B is larger and the explanation is something like:
"The value 750 is halfway between 850 and 650. However, because the (distribution) curve is decreasing in that interval (the interval after the 50th percentile), the area between 650 and 750 is greater than the area between 750 and 850. Since the value at the 75th percentile should divide in half the AREA between the value at the 60th percentile and the value at the 90th percentile, this value is closer to 650 than to 850."

I've been struggling with this for so long now and believe its wrong what they say. Yes, the AREA between the 60th and 90th percentile should be divided in half at the 75th percentile. However, this can't give me ANY indication about what the variable X will be at the 75th percentile, right?
Thank you very much for any answer!

Last edited by Carcass on 11 Feb 2018, 02:16, edited 1 time in total.
Edited by Carcass
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Re: Quant Comparison, OG Guide, wrong answer? [#permalink] New post 09 Feb 2018, 13:22
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Generally speaking, I don't ever see incorrect answers by ETS. Remember, they get to send test out their questions on hundreds of thousands of students in the experimental sections, essentially using them as copy editors. So any flaws will be detected before they put it in any official publications.

Anyway, look at it this way. 75th percentile is exactly halfway between 60th and 90th. Pretend the thing we're measuring is some kind of test score. In any normal curve, we expect the same number of people to score between 60th and 75th as between 75th and 90th. However, since it's a normal curve, the score at 75th percentile itself won't be exactly halfway between 650 and 850. Instead, we expect it to be below 750, since more people will be scoring near the average score than people scoring near the maximum score.

In other words, in a normal curve, a lot of values are piled up near the average, so if you increase the percentile by a set amount each time, the value won't change by much if you're near the average, but it'll change by more and more as you approach the extremes. So I agree with ETS that the answer is B, since the real value at 75th percentile, whatever it is, must be below 750.
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Re: Quant Comparison, OG Guide, wrong answer? [#permalink] New post 10 Feb 2018, 01:42
SherpaPrep wrote:
Generally speaking, I don't ever see incorrect answers by ETS. Remember, they get to send test out their questions on hundreds of thousands of students in the experimental sections, essentially using them as copy editors. So any flaws will be detected before they put it in any official publications.

Anyway, look at it this way. 75th percentile is exactly halfway between 60th and 90th. Pretend the thing we're measuring is some kind of test score. In any normal curve, we expect the same number of people to score between 60th and 75th as between 75th and 90th. However, since it's a normal curve, the score at 75th percentile itself won't be exactly halfway between 650 and 850. Instead, we expect it to be below 750, since more people will be scoring near the average score than people scoring near the maximum score.

In other words, in a normal curve, a lot of values are piled up near the average, so if you increase the percentile by a set amount each time, the value won't change by much if you're near the average, but it'll change by more and more as you approach the extremes. So I agree with ETS that the answer is B, since the real value at 75th percentile, whatever it is, must be below 750.


Hi SherpaPrep,

thank you very much for the explanation. I guess looking at it your way (more people tend to score towards the average score) helped more than the official answer.
I still think its a bad question. Hope I'll be spared such questions on test day :-)
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Re: Quant Comparison, OG Guide, wrong answer? [#permalink] New post 10 Feb 2018, 10:51
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@Matteo91 Yeah, to clarify a bit: there aren't really any bad official questions. However, there are a ton of bad official answers. Think about ETS's motivation. Their questions need to be perfect, with no ambiguity, so that no one has any cause to question their score or the GRE in general.

Answering their own questions, however, is a totally different situation. How do they make money? By charging you for the GRE, which is pretty expensive. So ETS isn't super motivated to show you the best way of solving problems. They'll certainly show a way to solve it, but not necessarily the fastest or easiest way. They'd love it if you studied their answers and then didn't get any better and wound up taking the GRE three times. Long story short: trust their questions, but don't rely on their answer explanations.
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Re: The random variable X is normally distributed. [#permalink] New post 11 Feb 2018, 02:28
Expert's post
Please guys,

to help the entire community, first, and you when you post a question is useful, strongly advisable if not mandatory do the followuing things


Actually, they are few things (barely two) to give to the question the right looking. After all, in every book, pdf you can have the format of the same is in this way.
Moreover, the question has been posted on the board. We do have all the OG questions in our directories. See here for reference The Official Guides for the GRE © - The Holy Grail as an announcement. We are working hard constantly to set up the best environment for the students.

The question is here, should be advised to continue the discussion there. https://greprepclub.com/forum/the-rando ... -1726.html

Thank you for your collaboration.

Regards
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Re: Quant Comparison, OG Guide, wrong answer? [#permalink] New post 11 Feb 2018, 04:03
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SherpaPrep wrote:
@Matteo91 Yeah, to clarify a bit: there aren't really any bad official questions. However, there are a ton of bad official answers. Think about ETS's motivation. Their questions need to be perfect, with no ambiguity, so that no one has any cause to question their score or the GRE in general.

Answering their own questions, however, is a totally different situation. How do they make money? By charging you for the GRE, which is pretty expensive. So ETS isn't super motivated to show you the best way of solving problems. They'll certainly show a way to solve it, but not necessarily the fastest or easiest way. They'd love it if you studied their answers and then didn't get any better and wound up taking the GRE three times. Long story short: trust their questions, but don't rely on their answer explanations.



I agree totally. At the end of the day, it is just a matter of business. Even the GMAT is so. Gmat has the advantage of having tonsssssss of official questions and ETS instead recycles OG after OG.

There are pro and cons in every exam.
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Re: The random variable X is normally distributed. [#permalink] New post 12 Feb 2018, 00:59
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Carcass wrote:
Please guys,

to help the entire community, first, and you when you post a question is useful, strongly advisable if not mandatory do the followuing things


Actually, they are few things (barely two) to give to the question the right looking. After all, in every book, pdf you can have the format of the same is in this way.
Moreover, the question has been posted on the board. We do have all the OG questions in our directories. See here for reference The Official Guides for the GRE © - The Holy Grail as an announcement. We are working hard constantly to set up the best environment for the students.

The question is here, should be advised to continue the discussion there. https://greprepclub.com/forum/the-rando ... -1726.html

Thank you for your collaboration.

Regards


Hi Carcass, thanks for the advice.
This was not intended to be posted as a question, I therefore thought I'll just open a new thread to discuss the answer.
Should've searched better for the question, thanks for the link!
I'll be doing a better job next time :-D
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Re: The random variable X is normally distributed. [#permalink] New post 12 Feb 2018, 16:26
Dont forget the curve is normally distributed... it's part of question
Re: The random variable X is normally distributed.   [#permalink] 12 Feb 2018, 16:26
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