If X and Y are the marks scored by a student in mid-sem and end-sem independently. Assume mid-sem marks and end-sem marks follow 2 distribution with degrees of freedom 3 and 6. A student is evaluated only on these two exams and the student passes if the sum total of his/her marks is greater than 9.342. Find the probability that in a class of 50 students, at least 30 pass?
2026-05-05 14:09:37.1777990177
probability chi-square distribution
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Here is a hint for this question:
The sum of the two chi-square distribution follows chi-square distribution with degree of freedom 9.
For the approach of this question, you can first get the probability of one student passes (with a score of greater than 9.342); then, use binomial distribution to get at least 30 of them pass.