Let A is the sum of the digits of your AUM student ID number, B is average of the digits of your AUM student ID number, and C is the first two digits of your AUM student ID number. For example, if your student ID is 43679, then your A= 4+3+6+7+9=29, B =(4+3+6+7+9)/5=5.8 and C = 43. A= B= C= Question 1 (25 points, 5 points each part): The time for a professor to grade an exam is normally distributed with a mean of A minutes and a standard deviation of B minutes. a) What is the probability that a randomly selected exam will require between 1 1 and 15 minutes to grade? b) What is the probability that a randomly selected exam will require more than 17 minutes to grade? c) What is the probability that a randomly selected exam will require less than 15 minutes to grade? d) Find x such that P(X C) d) P(20.5