Problem 20. (1 point) The professor of a introductory calculus 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 = 64% and a standard deviation of o = 11%. If using/finding z-values, use three decimals. (a) What is the probability that a random chosen final exam mark in this course will be at least 71%? 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 5% 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 of at least an A in the course. % (d) Suppose this professor randomly picked 29 final exams, ob- serving the earned mark on each. What is the probability that 3 of these have a final exam grade of less than 50%? Use four decimals in your