A test is graded on the scale 0 to 1, with 0.55 needed to pass. Student scores are modeled by the following density: f(x) = 4x 4 0 - 4x for 0≤x≤ 1/2 for 1/2 ≤ x ≤ 1 otherwise (a) What is the probability that a random student passes the exam? (b) What score is the 87.5 percentile of the distribution?

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A test is graded on the scale 0 to 1, with 0.55 needed to pass.
Student scores are modeled by the following density:
f(x) =
4x
4
0
-
4x
for 0 ≤ x ≤ 1/2
for 1/2 ≤ x ≤ 1
otherwise
(a) What is the probability that a random student passes the exam?
(b) What score is the 87.5 percentile of the distribution?
Transcribed Image Text:A test is graded on the scale 0 to 1, with 0.55 needed to pass. Student scores are modeled by the following density: f(x) = 4x 4 0 - 4x for 0 ≤ x ≤ 1/2 for 1/2 ≤ x ≤ 1 otherwise (a) What is the probability that a random student passes the exam? (b) What score is the 87.5 percentile of the distribution?
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