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 u = 64 % and a standard deviation of o = 10%. %3D %3D 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 72%? Answer to four decimals. 0.2119 (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. 0.0808 (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 of at least an A in the course. 82.81 田 % (d) Suppose this professor randomly picked 29 final exams, observing the earned mark on each. What is the probability that 6 of these have a final exam grade of less than 50%? Use four decimals in your answer. 0.0443

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