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(5 points) The professor of a Statistics class has stated that, historically, the distribution of final exam grades in the course resemble a Normal distribution with a mean final exam mark of u = 61% and a standard deviation of o = 12%. (a) What is the probability that a random chosen final exam mark in this course will be at least 73%? Answer to four decimals. (b) In order to pass this course, a student must have a final exam mark of at least 50%. What proportion of students will not pass the calculus final exam? Use four decimals in your answer. (c) The top 3% of students writing the final exam will receive a letter grade of at least an A in the course. To two decimal places, find the minimum final exam mark needed on the calculus final to earn a letter grade at least an A in the course. % (d) Suppose this professor randomly picked 27 final exams, observing the earned mark on each. What is the probability that 3 of these have a final exam grade of less than 61%? Use four decimals in your answer.