# 07_10ans - STAT 410 Examples for Summer 2009 1 A large...

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STAT 410 Examples for 07/10/2009 Summer 2009 1. A large class took two exams. Suppose the exam scores X (Exam 1) and Y (Exam 2) follow a bivariate normal distribution with μ 1 = 70, σ 1 = 10, μ 2 = 60, σ 2 = 15, ρ = 0.6. a) A students is selected at random. What is the probability that his/her score on Exam 2 is over 75? P ( Y > 75 ) = P ( Z > 15 60 75 - ) = P ( Z > 1.00 ) = 0.1587 . b) Suppose you're told that a student got a 80 on Exam 1. What is the probability that his/her score on Exam 2 is over 75? Given X = 80, Y has Normal distribution with mean ( 29 70 80 10 15 6 . 0 60 - + = 69 and variance ( 2 2 15 6 . 0 1 - = 144 ( standard deviation 12 ) . P ( Y > 75 | X = 80 ) = P ( Z > 12 69 75 - ) = P ( Z > 0.50 ) = 0.3085 . c) Suppose you're told that a student got a 66 on Exam 1. What is the probability that his/her score on Exam 2 is over 75? Given X = 66, Y has Normal distribution with mean ( 29 70 66 10 15 6 . 0 60 - + = 56.4 and variance ( 2 2 15 6 . 0 1 - = 144 ( standard deviation 12 ) . P ( Y > 75 | X = 66 ) = P ( Z > 12 4 . 56 75 - ) = P ( Z > 1.55 ) = 0.0606 .

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d) Suppose you're told that a student got a 70 on Exam 2. What is the probability that his/her score on Exam 1 is over 80?
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