(1 point) The professor of a introductory calculus class has stated that, historically, the distribution of...

(1 point) The professor of a introductory calculus class has stated that, historically, the distribution of test grades in the course resemble a Normal distribution with a mean test mark of ?=63μ=63% and a standard deviation of ?=9σ=9%.

If using/finding ?z-values, use three decimals.

(a) What is the probability that a random chosen test 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 test mark of at least 50%. What proportion of students will not pass the calculus test? Use four decimals in your answer.

(c) The top 6% of students writing the test will receive a letter grade of at least an A in the course. To two decimal places, find the minimum test 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 tests, observing the earned mark on each. What is the probability that 5 of these have a test grade of less than 50%? Use four decimals in your answer.

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