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Scores in an exam to measure understanding of probability before a class is taught at a...

Scores in an exam to measure understanding of probability before a class is taught at a university have an average of 35 with standard deviation 5. After the course is taught, the average exam score is 80 with standard deviation 6. There is a correlation between the pre-class and post-class score of 0.7. The scores are jointly distributed according to the bivariate normal distribution.

(a) What is the probability that the post-course score (the score after the course has been taken) is larger than 90?

(b) What is the probability that for those who score 45 in the pre-course test, the score is larger than 90 in the post course test?

(c) What is the variance of the sum of the pre and post-course scores?

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