Percentiles question

[katherine.st.onge]

I'm having trouble understanding why Quantity B is greater in this problem....

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.

A: The value of the 75th percentile of the distribution of x
B: 750

Thanks!

[jgabry]

Hey Katherine,

This is a tricky question.

The graph of a normal distribution is symmetric with the bulk of the area under the curve occurring near the mean. The 75th percentile does fall exactly between the 60th and the 90th, but in terms of area under the curve and not in terms of the value associated with the percentile (in this case 650 and 850).



As we can see in the picture, as we get farther away from the mean the area under any given segment of the curve becomes less and less. Therefore, in the scenario we have in this question, there will be more area under the curve between 650 and 750 than between 750 and 850.

The value of the 75th percentile will be wherever half of the area falls between 650 and 850. This will be closer to 650 than to 850 because there is more area near 650 than 850. If it's closer to 650 than 850 it must be less than 750. So the answer is that 750 is greater, which corresponds to choice B.

Does that help? Sorry if my explanation was confusing...

[tommywallach]

Hey All,

Great explanation here. Also worth adding is just a rule of the GRE. There's no way the answer to this question would be C. It's just too easy/obvious. So once you tell yourself that ("Self, the answer cannot be C."), you can start looking for the reason why things would shift here. Also, never be afraid to draw that curve, just to scope it out visually, when doing a distribution question.

-t