# QZ 2-C - The department has to pay a \$5 delivery fee(the...

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STAT 400 Fall 2011 Version C Name ANSWERS . Quiz 2 (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. Suppose the number of boxes of Hammermill paper used by Anytown College Statistics & Probability Department each month is random and has the following probability distribution: x f ( x ) x f ( x ) x 2 f ( x ) 0 0.1 0 0 1 0.1 0.1 0.1 2 0.3 0.6 1.2 3 0.3 0.9 2.7 4 0.2 0.8 3.2 2.4 7.2 Suppose at the end of each month the department orders the same number of boxes as was used during the month. Suppose each box costs \$25.
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Unformatted text preview: The department has to pay a \$5 delivery fee (the delivery fee does not depend on the number of boxes ordered). Then the monthly “paper” bill is Y = 25 ⋅ X + 5. Find Anytown College Statistics & Probability Department’s average monthly “paper” bill and its standard deviation. E ( X ) = ∑ ⋅ x x f x all ) ( = 2.4 . [ ] [ ] 2 all 2 2 2 X E ) ( X E X E X Var ) ( ) ( ) ( ) (-=-= ∑ ⋅ x x f x = 7.2 -( 2.4 ) 2 = 1.44 . SD ( X ) = 44 . 1 = 1.2 . E ( Y ) = 25 ⋅ E ( X ) + 5 = 25 ⋅ 2.4 + 5 = \$65 . SD ( Y ) = | 25 | ⋅ SD ( X ) = 25 ⋅ 1.2 = \$30 ....
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