The random variable X is normally distributed

Sam Kinsman

Hi Kody,

Unfortunately, that won't work. When a set of numbers is normally distributed, that does not mean that they are equally spaced out. So if we have the 90th percentile, and multiply by 1.1, that will not give us the 100th percentile.

You may find it helpful to review the following two blog posts about normal distribution:

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

https://magoosh.com/statistics/understanding-normal-distribution/

I hope this helps!

Best,
Sam

Jun 12, 2018 • Reply

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