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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