One hundred students are writing the final exam in Dr. Strangepork's course on statistics. The mean score on the final exam is 54 with a standard deviation of 8. Treat these as population parameters. a) Drawing a student at random from the class, what is the probability that their score will be greater than 56 and less than 66 (5 marks)? b) Drawing a student at random from the class, what is the probability that their score will be either less than 50 OR greater than 60 (5 marks)? c) What grade is associated with the 80th percentile (3 marks)? d) Dr. Strangepork decides to rescale the grades so that the new mean will be 70 and the new standard deviation will be 11. If the old score is 46, what would the new scaled score be (4 marks)?