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Unformatted text preview: and variance Var ( X Y ) = Var ( X ) + Var ( Y ) = 0.20 2 + 0.15 2 = 0.0625 ( standard deviation = $0.25 ). P ( X Y < 0 ) = < 25 . 30 . Z P = P ( Z < 1.20 ) = ( 1.20 ) = 0.1151 . b) (5) Alex is planning a MilkandOreos party for his imaginary friend. He buys 4 gallons of milk and 7 packages of Oreo cookies. Find the probability that he paid less than $30. That is, find P ( 4 X + 7 Y < 30 ). 4 X + 7 Y has Normal distribution with mean E ( 4 X + 7 Y ) = 4 3.00 + 7 2.70 = $30.90 and variance Var ( 4 X + 7 Y ) = 16 Var ( X ) + 49 Var ( Y ) = 16 0.20 2 + 49 0.15 2 = 1.7425 ( standard deviation $1.32 ). P ( 4 X + 7 Y < 30 ) = < 32 . 1 90 . 30 30 Z P = P ( Z < 0.68 ) = ( 0.68 ) = 0.2483 ....
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 Spring '08
 Kim
 Statistics, Probability

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