The grade of a course is based on two exams: the midterm and the final, each of 100 points maximum and counts 50% of the grade. The professor grades the midterm by randomly assigning each student a score independently of other scores of mean 73 and standard deviation (which is the square root of the variance) of 15. The professor grades the final by randomly assigning each student a score independently of other scores of mean 68 and standard deviation of 10. The number of students in the class is 64. 1. Estimate the probability that the midterm class average is 70% or more.
2. Estimate the probability that the final class average is 70% or more.
3. Estimate the probability that the course class average is 70% or more.
Use the Central Limit Theorem.