Please show in R programiming

3. Suppose that we wish to predict your grade in DS 612 based on the number of hours you study each week. Assume in MBA classes 20% get A, 50% get B and 30% get C. Also assume that on average, A students study 5 hours/week for each course, B students study 3 hours/week and C students study 1 hour week. Assume the pooled standard deviation of number of hours students study is 1 hour. Also assume that the number of hours students study for the class follow a normal distribution. Predict the probability that a student with 5 hours of study time per week get an A in the course. (X is the last digit of your student number, if your last digit is 0, use 5) Hint( You can either use discriminant scores or the bayes theorem to solve this question) (15 points)