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 μ=63μ=63% and a
standard deviation of σ=9σ=9%.
If using/finding zz-values, use three decimals.
(a) What is the probability that a random chosen
final exam 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 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, 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.
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