Grades of a class are based entirely on midterm and final exams. In all, the exams have 100 separate parts, each worth 5 points. A student scoring at least 85%, is guaranteed an A+ score. Throughout this problem, consider a particular student who, based on performance in other courses and amount of effort put into the class, is estimated to have a 90% chance to complete any particular part of exam correctly. Parts not completed correctly receive zero credit. (a) Assume that the scores on different parts are independent. Based on the Law of Large Numbers, about what total score for the semester are we likely to see? (b) Using the Central Limit Theorem, calculate the approximate probability the student scores enough points for a guaranteed A+ score.