Question: A test is graded on the scale 0 to 1, with 0.55 needed to pass. Student scores are modelled by the following density: f (

A test is graded on the scale 0 to 1, with 0.55 needed to pass. Student scores are

modelled by the following density:

f(x) = 4x for 0 x and = 4 - 4x for 1/2 x 1; 0 otherwise

(i) What is the probability that a random student passes the exam?

(ii) What score is the 87.5 percentile of the distribution?

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