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In distribution of 850 different measurements, x centimeters

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In distribution of 850 different measurements, x centimeters [#permalink] New post 25 Jun 2016, 06:35
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In a distribution of 850 different measurements, x centimeters is at the 73rd percentile. If there are 68 measurements in the distribution that are greater than y centimeters but less than x centimeters, then y is approximately at what percentile in the distribution?


A. 45th
B. 50th
C. 55th
D. 60th
E. 65th

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Re: In distribution of 850 different measurements, x centimeters [#permalink] New post 25 Jun 2016, 06:38
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Explanation

If x centimeters is at the 73rd percentile, then approximately 73% of the measurements in the distribution are less than or equal to x centimeters. The 68 measurements that are greater than y centimeters but less than x centimeters are \frac{68}{850}*100%, or 8%, of the distribution. Thus approximately 73% – 8%, or 65%, of the measurements are less than or equal to y centimeters, that is, y is approximately at the 65th percentile in the distribution. The correct answer is Choice E.
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Re: In distribution of 850 different measurements, x centimeters [#permalink] New post 08 Jan 2017, 12:12
sorry,i couldn't understand this question !!
if there is more simple clarification plz
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Re: In distribution of 850 different measurements, x centimeters [#permalink] New post 12 Jan 2017, 17:41
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awamy wrote:
sorry,i couldn't understand this question !!
if there is more simple clarification plz



There are 68 measurements between x and y. Now if x is at 73% what is % corresponding to y.

Since \frac{68}{850} \times 100 = 8% so % corresponding to y is 73% - 8% = 65%

Hence option E or 65% is correct.
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Re: In distribution of 850 different measurements, x centimeters [#permalink] New post 25 Jan 2017, 10:57
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sandy wrote:
In a distribution of 850 different measurements, x centimeters is at the 73rd percentile. If there are 68 measurements in the distribution that are greater than y centimeters but less than x centimeters, then y is approximately at what percentile in the distribution?

A. 45th
B. 50th
C. 55th
D. 60th
E. 65th


In a distribution of 850 different measurements, x centimeters is at the 73rd percentile.
73% of 850 = 620.5, which is approximately 621
So, we know that approximately 621 measurements are less than x (and the other 229 measurements are greater than x).
We might sketch it as follows:
-------621 measurements----------x------229 measurements


There are 68 measurements in the distribution that are greater than y centimeters but less than x centimeters
We can add this to our sketch as follows:
-------553 measurements-------y----68 measurements----x------229 measurements

Notice that there are 621 measurements less than x, AND there are 68 measurements between y and x.
621 - 68 = 553 .
So, we can conclude that 553 measurements are less than y

y is approximately at what percentile in the distribution?
553 of the 850 measurements are less than y.
553/850 ≈ 65%

Answer: E
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Re: In distribution of 850 different measurements, x centimeters [#permalink] New post 25 May 2017, 07:58
why is it reasonable that the distribution is assumed to be uniform? i.e what are the clues that tell the distribution is uniform?
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Re: In distribution of 850 different measurements, x centimeters [#permalink] New post 25 May 2017, 08:09
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ayi wrote:
why is it reasonable that the distribution is assumed to be uniform? i.e what are the clues that tell the distribution is uniform?


We don't need a uniform distribution to answer this question. The percentiles are sufficient to arrive at the correct answer.

Cheers,
Brent
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Re: In distribution of 850 different measurements, x centimeters   [#permalink] 25 May 2017, 08:09
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