Question

On stat your assessment is based on: Final Exam 47% Learn based on‐line assessment 34% Assignments 19%

Consider three random variables X, Y and Z which respectively represent the exam, on‐line assessment total and assignment scores (out of 100%) of a randomly chosen student. Assume that X, Y and Z areindependent (this is clearly not true, but the answers may be a reasonable approximation).

Suppose that past experience suggests the following properties of these assessment items (each out of 100%): E(X) = 61, sd(X) = 20, E(Y) = 72, sd(Y) = 22 and E(Z) =65, sd(Z) = 24.

a) Find the distribution parameters, E(T) and Var(T), for the total mark, T, where:T = 0.47X+0.34Y+0.19Z.

b) Assume the on‐line assessment, exam and assignment scores are Normally distributed. If the pass mark is 50%, calculate the probability that a randomly selected student will pass.

c) Find the expected number of A+ grades (90% and above) to be awarded in July if there are 840 students on the course this semester.

d) If a random sample of 16 stat students is selected, what is the probability that their average grade is at least a B (that is, on average they get 70% or more in total)?

if you could potentially show how to work it out on excel as well, that would be great

Answer 1

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pl 군 > 1.4008561 C O866 PLAvecnoge S 80806