The length ofti me required by students to complete a 1-hour exam is a random va

Question

The length ofti me required by students to complete a 1-hour exam is a random variable, Y, with a density function given by

f(y)= {(3/2)y^2+y,   0<=y<=1

        {             0,    elsewhere

a. find the probability that random selected student will finish the test in less that 15 minutes

b. given that a particular student needs a least 15 minutes to complete the exam, find the probability that she will require at least 45 minutes to finish the exam

c. find the mean needed to finish the test.

please explain your answers!

Explanation / Answer

a) ans = integral((3/2)y^2+y dy) from y=0 to 0.25 , because 15 min = 1/4 hour

= 0.039

b) P(Y>=0.75) / P(Y >=0.25) =integral((3/2)y^2+y dy) from y=0.75 to 1 divided by (1-0.039)

= 0.507813 /( 1 -0.039) = 0.52842

c ) mean = integral (y * [(3/2)y^2+y]) y goes from 0 to 1

= 0.708333 hours

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