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QZ 2-D - permit to sell shells Let Y denote Sally’s daily...

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STAT 400 Fall 2011 Version D 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. Sally sells seashells by the seashore. The daily sales X of the seashells have the following probability distribution: x f ( x ) x f ( x ) x 2 f ( x ) 0 0.15 0 0 1 0.30 0.30 0.30 2 0.30 0.60 1.20 3 0.20 0.60 1.80 4 0.05 0.20 0.80 1.70 4.10 Suppose each shell sells for $10.00. However, Sally must pay $3.00 daily for the
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Unformatted text preview: permit to sell shells. Let Y denote Sally’s daily profit. Then Y = 10 ⋅ X – 3. Find Sally’s expected daily profit and its standard deviation. E ( X ) = ∑ ⋅ x x f x all ) ( = 1.70 . [ ] [ ] 2 all 2 2 2 X E ) ( X E X E X Var ) ( ) ( ) ( ) (-=-= ∑ ⋅ x x f x = 4.10 -( 1.70 ) 2 = 1.21 . SD ( X ) = 21 . 1 = 1.10 . E ( Y ) = 10 ⋅ E ( X ) – 3 = 10 ⋅ 1.70 – 3 = $14 . SD ( Y ) = | 10 | ⋅ SD ( X ) = 10 ⋅ 1.10 = $11 ....
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