Consider a student taking a 4 year BTech course in IIT Jammu. Let there be an efficiency score (EF) falling in the range [0, 50]. The students who are able to complete the course in 4 years have EF scores following a normal distribution with mean 30, and std 5. The students who are not able to complete the course in 4 years also have EF scores following normal distribution with mean 20 and std 4. Let G be the event that the student graduates in 4 years and let nG be the event that he does not graduate in 4 years. Suppose that 80% of the students who take admission are able to complete their graduation within 4 years. Let x denote the EF score of the student. [10] a) Then what is the probability that a student will graduate in 4 years given his EF score is x=25? b) How will you find out the min EF score that maximizes the probability that a student graduates in 5 years. First frame your problem, outline all major notations and solve step wise to show the results.