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Could anyone please help me! I am really confused.
There is question in Official guide with detailed explanation and the same type in Manhattan 5lb wit different explanation.
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- morvarid2191
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- tommywallach
- Manhattan Prep Staff
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- Joined: Thu Mar 31, 2011 11:18 am
Re: percentile question
Hey Morvarid,
In the future, please just type the text of the question into the forum, so we can see it. I'll do that here.
The random variable X is normally distributed. The values 650 and 850 are at the 60th and 90th percentiles of the distribution of X, respectively.
Quantity A: The value at the 75th percentile of the distribution of X
Quantity B: 750
The first thing to notice on this question is that the answer is just NOT going to be C. That would be way too easy (halfway between 60 and 90 is 75, so halfway between 650 and 850 is 750...done?). Remember, the GRE is a friendly test, but it's not that friendly!
Instead, it should be your job to figure out why the answer is not right in the middle. In this case, it's because every percentile group in a normal distribution has FEWER people in it the farther it gets from the mean. That's the nature of the bell curve. Only a few people get top "scores" and only a few people get bottom "scores."
So if you take the 50th to the 55th percentiles (as a random example), that group of scores would include more people than the 95th to the 100th percentile (for what are probably self-explanatory reasons--it's easier to get a 50th percentile score than 95th percentile score). That means that the number of people who score in the 60th-75th percentile score area will be greater than the number of people who score in the 75th to 90th score area. This is why the answer here is closer to 650. The lower the score, the more people will be included.
Hope that helps!
-t
In the future, please just type the text of the question into the forum, so we can see it. I'll do that here.
The random variable X is normally distributed. The values 650 and 850 are at the 60th and 90th percentiles of the distribution of X, respectively.
Quantity A: The value at the 75th percentile of the distribution of X
Quantity B: 750
The first thing to notice on this question is that the answer is just NOT going to be C. That would be way too easy (halfway between 60 and 90 is 75, so halfway between 650 and 850 is 750...done?). Remember, the GRE is a friendly test, but it's not that friendly!
Instead, it should be your job to figure out why the answer is not right in the middle. In this case, it's because every percentile group in a normal distribution has FEWER people in it the farther it gets from the mean. That's the nature of the bell curve. Only a few people get top "scores" and only a few people get bottom "scores."
So if you take the 50th to the 55th percentiles (as a random example), that group of scores would include more people than the 95th to the 100th percentile (for what are probably self-explanatory reasons--it's easier to get a 50th percentile score than 95th percentile score). That means that the number of people who score in the 60th-75th percentile score area will be greater than the number of people who score in the 75th to 90th score area. This is why the answer here is closer to 650. The lower the score, the more people will be included.
Hope that helps!
-t
2 posts Page 1 of 1