The length of time for students to complete a 1-hour timed standardized mathematics test has a probability density function f(t) = 1.5t2 + t,    0 ≤ t ≤ 1 where t is the time in hours. (Round your answers to three decimal places.) (a) Find the probability that the time it takes a randomly selected student to complete the test is more than 45 minutes.   (b) Find the probability that the time it takes a randomly selected student to complete the test is more than 15 minutes given that it is less than 45 minutes.

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