Question

The professor of a Statistics class has stated that, historically, the distribution of test grades in the course resembles a Normal distribution with a mean test mark of μ=61% and a standard deviation ofσ=9%.

(a) What is the probability that a randomly 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 3% 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 28 tests, observing the earned mark on each. What is the probability that 3 of these have a test grade of less than 61%? Use four decimals in your answer.

Answer 1