Source: Official Guide Revised GRE 1st Ed. Part 6; Set 3; #5

13

The random variable X is normally distributed

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

3 Explanations

2

Yu Charles

I don't know what is the meaning of values at 60th and 90th? From the graph, it value at 90th should be lower then that at 60th. Could you give me an explanation about the value?

Apr 5, 2016 • Comment

Cydney Seigerman, Magoosh Tutor

Hi Charles :)

Firstly, to better understand the fundamental concepts of normal distributions, which are being tested in this question, I highly recommend checking out the following post on our blog.

http://magoosh.com/gre/2012/normal-distribution-on-the-gre/

The percentile refers to the percentage of the population below the value of interest. In this case, the value at the 60th percentile is higher than 60 percent of the population, while the value at the 90th percentile is higher than 90 percent of the population. As you can see, the higher the percentile, the higher the value. That said, in a normal distribution, as we move away from the mean (50th percentile), the number of values at a given percentile decreases. In other words, there are fewer values at the 90th percentile than at the 60th percentile, while the magnitude at the 90th percentile is greater than that at the 60th percentile.

We can make a similar observation on the other side of the mean. The farther away a value is from the mean, the fewer number of entries that have that value. For example, there will be fewer entries at the 2nd percentile than at the 30th percentile.

Does that make sense, Charles? I hope this helps clear up your doubts! :)

Apr 17, 2016 • Reply

Isabella Carbonell

Is this problem solvable if they ask us to find the 80th percentile instead? Does this mean that the 75th percentile of every normal distribution would be a number closer to the 60th percentile than to the 90th?

Apr 4, 2017 • Reply

Cydney Seigerman, Magoosh Tutor

Good questions, Isabella! Yes, the 75th percentile will always be closer to the 60th percentile in a normal distribution. A general definition is that the pth percentile is the value that has p% of the values below it. And for a normal distribution, the 50th percentile is the median, the 25th percentile is the 1st quartile (1 standard deviation below the mean) and the 75th percentile is the 3rd quartile (1 standard deviation about the mean).

The blog post I mentioned above and also this one (https://magoosh.com/gre/2012/standard-deviation-on-the-new-gre/) illustrate how there are more values closer to the mean than farther from the mean.

So, the key to this question is that 750 is halfway between 650 and 850 and we're comparing this with the 75th percentile, which will always be closer to 60th percentile than the 90th. Depending on the values we were asked to compare, we could compare the 80th percentile. However, that may look more complicated, as 80 is 2/3 between 60 and 90, so the number in question would be 133 1/3, following the pattern of the actual question.

Hope this helps!

Apr 8, 2017 • Reply

11

M O

But the question doesn't ask about 15th percentile. Where does this come from?

Jan 23, 2015 • Comment

8

Gravatar Chris Lele, Magoosh Tutor

Oct 7, 2012 • Comment

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