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# QZ 6-A - = \$0.30 and variance Var X – Y = Var X Var Y =...

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STAT 400 Fall 2011 Version A Name ANSWERS . Quiz 6 (10 points) Be sure to show all your work; your partial credit might depend on it. No credit will be given without supporting work. 1. In Anytown, the price of a gallon of milk ( X ) varies from day to day according to normal distribution with mean \$3.30 and standard deviation \$0.40. The price of a package of Oreo cookies ( Y ) also varies from day to day according to normal distribution with mean \$3.00 and standard deviation \$0.30. Assume the prices of a gallon of milk and a package of Oreo cookies are independent. a) (5) Find the probability that on a given day, the price of a package of Oreo cookies is higher than the the price of a gallon of milk. That is, find P ( Y > X ) . P ( Y > X ) = P ( X – Y < 0 ) . X – Y has Normal distribution with mean E ( X – Y ) = 3.30 – 3.00 = \$0.30
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Unformatted text preview: = \$0.30 and variance Var ( X – Y ) = Var ( X ) + Var ( Y ) = 0.40 2 + 0.30 2 = 0.25 ( standard deviation = \$0.50 ). P ( X – Y < 0 ) = -< 50 . 30 . Z P = P ( Z < – 0.60 ) = Φ ( – 0.60 ) = 0.2743 . b) (5) Alex is planning a Milk-and-Oreos party for his imaginary friend. He buys 2 gallons of milk and 5 packages of Oreo cookies. Find the probability that he paid less than \$20. That is, find P ( 2 X + 5 Y < 20 ). 2 X + 5 Y has Normal distribution with mean E ( 2 X + 5 Y ) = 2 ⋅ 3.30 + 5 ⋅ 3.00 = \$21.60 and variance Var ( 2 X + 5 Y ) = 4 ⋅ Var ( X ) + 25 ⋅ Var ( Y ) = 4 ⋅ 0.40 2 + 25 ⋅ 0.30 2 = 2.89 ( standard deviation = \$1.70 ). P ( 2 X + 5 Y < 20 ) = -< 70 . 1 60 . 21 20 Z P = P ( Z < – 0.94 ) = Φ ( – 0.94 ) = 0.1736 ....
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