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

[Tomacork]

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

 

[HallsofIvy]

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.

 

[Tomacork]

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?