MHB How many people will be in the top 10% in at least one examinations

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In a scenario where 100 people take two exams with a correlation of 0.6, 10 individuals would be expected in the top 10% of each exam, with 6 overlapping in both. This results in 19 people being in the top 10% for at least one exam. To calculate for more than two exams with varying correlations, the same principles apply, adjusting for the specific correlation values between each pair of exams. For three tests with correlations of 0.7, 0.6, and 0.5, a more complex calculation is needed to determine the number of individuals in the top 10% across all exams. Understanding these correlations is crucial for accurate predictions in multiple examination scenarios.
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If 100 people take two exams, the results of which correlate at .6, how many people will be in the top 10% in at least one examinations? I understand that if the exams were unrelated then we would expect one person to be in the top 10% for both groups,and therefore 19 people would be in in the top 10% in at least one exam. However, I don't know how to calculate this when the exams are correlated, nor how to calculate it if there is more than 2 examinations. Any help appreciated
 
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There will be, of course, 10% of 100= 10 people in the "top 10%" of each exam. If the tests "correlate at 0.6" we would expect 0.6 (10)= 6 people to be in the top 10% in both exams.
 
HallsofIvy said:
There will be, of course, 10% of 100= 10 people in the "top 10%" of each exam. If the tests "correlate at 0.6" we would expect 0.6 (10)= 6 people to be in the top 10% in both exams.

Thanks for that. It is simpler than I thought. I thought that the correlation between the examinations would need to be squared. How would I calculate this for more than 2 exams and with different correlations? For instance, how many people would be in the top 10% in three tests(A, B & C) which correlate at .7 for A/C, .6 for A/B and .5 for B/C?
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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