Exam Problem: calculating the overall distribution based on individual parts' distributions?


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Hi guys, hope you are enjoying the day!

So I am having this problem where I have a population of people that participated in a national examination process (N=20,500). The examination required each student to take 4 different tests A, B, C and D and then they would be graded on a scale of [0-20] for each test and an average of the four would form the final grade on a scale of 0 to 20. When the examination process was completed the competent autority uploaded the statistics showing what percentage of the students had scored in each grade category (0-5), (5-10), (10-11), (11-12), ..., (18-19) and (19-20) for every different test. No statistics where uploaded regarding the final score.

And here comes my question: I know in which grade bracket I belong for every of the four tests. Is it possible to calculate approximately in what percentile my overall score would be - based on the distributions of each of the four tests?