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 MilkandOreos 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 ....
View
Full Document
 Spring '08
 Kim
 Statistics, Normal Distribution, Probability, Standard Deviation, Variance, oreo cookies

Click to edit the document details