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practicefinal - STAT 400 Final Exam Practice Problems 1 A...

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STAT 400 Final Exam Practice Problems 1. A chain of video stores sells three different brands of VCRs. Of it’s VCR sales, 60% are brand 1 (the least expensive), 30% are brand 2, and 10% are brand 3. Each manufacturer offers a 1-year warranty on parts and labor. It is known that 25% of brand 1 VCRs require warranty work, whereas the corresponding percentages for brands 2 and 3 are 20%, 10%, respectively. (a) What is the probability that a randomly selected purchaser has bought a brand 1 VCR and the VCR will need repair while under warranty? (b) What is the probability that a randomly selected purchaser has a VCR that will need repair under warranty? (c) If a customer returns to the store with a VCR that needs warranty repair work, what is the probability that it is a brand 1 VCR? 2. (a) Suppose that math SAT scores for a particular population are normally distributed with mean 470 and a standard deviation of 100. i. Find the 33rd percentile, π 0 . 33 . ii. Given a random sample of size n = 10 scores, find P (450 < ¯ X < 550). (b) Suppose X 1 , X 2 , · · · , X 16 is a random sample of size 16 from N (0 , 1). Determine c , such that P ˆ 16 X i =1 X 2 i < c !
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