10. [-/6.66 Points] DETAILS WACKERLYSTAT7 4.2.017. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER The length of time required by students to complete a one-hour exam is a random variable with a density function given by 10, f(y ) = cy2 + y, 0sys1, elsewhere. (a) Find c. (b) Find F(y). y 1 (c) Graph f(y) and F(y). 3.0 3.0 2.5 2.5 2.0 f( y) F(y) F(y) 2.0 2.0 1.5 1.5 1.5 1.0 1.0 F(y) 1.0- 0.5 0.5 0.5 L X O 0.2 0.4 0.6 0.8 1.0 X O 0.2 0.4 0.6 0.8 1.0 X O 0.2 0.4 0.6 0.8 1.0O 0.2 0.4 0.6 0.8 1.0 O 0.2 0.4 0.6 0.8 1.0 O 0.2 0.4 0.6 0.8 1.0 2.5- 2.0 fly) 1.5 1.0 F(y) 0.5 X O 0.2 0.4 0.6 0.8 1.0 (d) Use F(y) in part (b) to find F(-1), F(0), and F(1). F(-1) = F(0) = F(1) = (e) Find the probability that a randomly selected student will finish in less than half an hour. (Round your answer to four decimal places.) (f) Given that a particular student needs at least 15 minutes to complete the exam, find the probability that she will require at least 30 minutes to finish. (Round your answer to four decimal places.) Need Help? Read It