Normal Distribution - Clarificaiton

GRE Quant Problem Solving
1

This was one of the questions I saw in the 5lb book:

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This was the solution provided for it:

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This solution to the above-mentioned problem revealed that I was not clear with the understanding of normal distribution.

Firstly, I considered an extreme example. If a person is at the 100th percentile in a class, does it mean that 100% of the class has scored less than him? This does not make sense to me as he is also a part of that 100% class strength. I thought that 99% of the class would be scoring less than him.

I applied the same logic over there and ended up thinking that 31% of the class should have scored less than John (as he is at the 32nd percentile). On the other hand, as Jane is at the 68th percentile, I thought 33% of the class should have scored equal to or greater than her (from 68 to 100 inclusive).

Where am I going wrong in this thought process? Can someone please help me with this as this is slowly eating my brain? :’) Thanks in advance!

2

You , are correct in your first assumption that no one can be in the 100% but in some cases if you do see a 100% they must have round things off(although I think 99% is mathematically correct representation ). i.e. if you score a 99 percentile in GRE verbal section that means you’re in the top 1% and 99% of the test takers have scored below you.

As for quantity A we are given that John is in 32 % and we asked how many received a score less than John : So , 32 % scores below John

Now, for quantity B : Jane score is in the 68% , so hence it means 68% have scored below jane and (100-68)% or 32 % have scored greater than or equal to Jane.

references:https://www.statisticshowto.com/probability-and-statistics/percentiles-rank-range/

1 Like
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Hello @HoldMyBeer, Thank you for your thoughts bro. I’ll look into the resource you have provided me for more insights. :slight_smile: