Question

Assume that there are four exams in a course and you think (before taking the exams) that your grade in each of the exams is a normal random variable with mean 74 and standard deviation 20. Assuming that the grades in different exams are independent, calculate the probability that you receive a grade higher than 57 in exactly one of these four exams.

Answer 1

Solution: Here given that there are four exams in a course and a course and the grade in each of the exams is a normal random venable with mean 74 and standard deviation 20 ieee 74 20 Here XN Normal (7420) To that you find the receie a probability grade higher than 57 in exactly one of these four exams. đ , P(x >=1)= PExow s 57 - 74 T 20. p[2)-0.85) By using standerd Nomed table we get 0.8023 PGX357)= 0.8023 Therefore the probability that you receive a grade higher than 57 in exactly these four exams is exactly one of 0.8023