(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

=64% and a standard deviation of=10

=10%.

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.

(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 of 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 4 of these have a final exam grade of less than 50%? Use four decimals in your answer.