Question
A student's grade in a course is determined by their scores on assignments, exams, and the number of missed class days. Suppose the final grade
A student's grade in a course is determined by their scores on assignments, exams, and the number of missed class days. Suppose the final grade is calculated as the total of 40% of the assignment score and 60% of the exam score, and reduced by 10% of the number of missed class days. For example, if a student earned 90 in assignments, 80 in exams, and missed 1 day of class, his/her final score is 0.4*90 + 0.6*80 - 0.1*1 = 83.9.
From historical data we know that the assignment score has mean of 85 and standard deviation of 10; and the exam score has mean of 80 and standard deviation of 15. We also know that the mean and standard deviation of missed class days are 2 and 0.5.
What are the mean and standard deviation of the final score, assuming the assignment score, exam score, and number of missed class days are independent?
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