Quiz2 - STA3032 Section 7347 Quiz 2 Solution 1-2 An...

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STA3032 Section 7347 Quiz 2 Solution 1-2. An appliance dealer sells three different models of upright freezers having 13 . 5, 15 . 9 and 19 . 1 cubic feet of storage space respectively. Let X = the amount of storage space purchased by the next customer to buy a freezer. The price of a freezer having capacity X cubic feet is 25 X - 8 . 5. Suppose that X has p.m.f. x 13 . 5 15 . 9 19 . 1 p(x) 0 . 2 0 . 5 0 . 3 E(X) = X all x x · p ( x ) = 13 . 5 × 0 . 2 + 15 . 9 × 0 . 5 + 19 . 1 × 0 . 3 = 16 . 38 Var(X) = X all x x 2 · p ( x ) - (E(X)) 2 = (13 . 5) 2 × 0 . 2 + (19 . 1) 2 × 0 . 5 + (19 . 1) 2 × 0 . 3 - (16 . 38) 2 = 272 . 298 - (16 . 38) 2 = 3 . 9936 SD(X) = p Var(X) = 1 . 9984 Y = the price of a freeze having capacity X = 25 X - 8 . 5 1. What is the expected price paid by the next customer to buy a freezer? (c) 401 : E(Y) = 25 × E(X) - 8 . 5 = 25 × 16 . 38 - 8 . 5 = 401 2. What is the standard deviation of the price paid by the next customer to buy a freezer? (e) 49.9600 : Var(Y) = 25 2 × Var(X) = 25 2 × 3 . 9936 = 2496 SD(Y) = p Var(Y) = 2496 = 49 . 9600 1
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3. Tests for impurities commonly found in drinking water from private wells showed that 30% of all wells in a particular county have impurity A . If a randomly sample of five wells is selected from the large number of wells in the county, what is the probability that of observing at least three wells containing impurity A ? (a) 0.1631 : X = the number of wells that contain impurity A X Bin(5 , 0 . 3) P ( X 3) = P ( X = 3) + P ( X = 4) + P ( X = 5) = 0 . 1323 + 0 . 0284 + 0 . 0024 = 0 . 1631 4. Assume that hitting oil at one drilling location is independent of success at another
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