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

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SUMMARY

In a scenario where 100 individuals take two correlated exams with a correlation coefficient of 0.6, 10 individuals will be in the top 10% for each exam, resulting in an expected 19 individuals in the top 10% for at least one exam. The calculation for those in the top 10% for both exams is derived from multiplying the correlation coefficient by the number of individuals in the top 10%, yielding 6 individuals. For multiple exams with varying correlations, further calculations are necessary to determine the total number of individuals in the top 10% across all exams.

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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?
 

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