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Pr2 - STAT 410 Practice Problems for 3.4 and 3.5 Spring...

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STAT 410 Practice Problems for 3.4 and 3.5 Spring 2008 1. A gas station sells three grades of gasoline: regular unleaded, extra unleaded, and super unleaded. These are priced at $1.55, $1.70, and $1.85 per gallon, respectively. Let X 1 , X 2 , and X 3 denote the amounts of these grades purchased (gallons) on a particular day. Suppose the X i ’s are independent with μ 1 = 1,000, μ 2 = 500, μ 3 = 300, σ 1 = 100, σ 2 = 80, and σ 3 = 50. If the X i ’s are normally distributed, what is the probability that revenue exceeds … a) $2,600? b) $3,000? 2. Suppose that the actual weight of "10-pound" sacks of potatoes varies from sack to sack and that the actual weight may be considered a random variable having a normal distribution with the mean of 10.2 pounds and the standard deviation of 0.6 pounds. Similarly, the actual weight of "3-pound" bags of apples varies from bag to bag and that the actual weight may be considered a random variable having a normal distribution with the mean of 3.15 pounds and the standard deviation of 0.3 pounds. A boy-scout troop is planning a camping trip. If the boy-scouts buy 3 "10-pound" sacks of potatoes and 4 "3-pound" bags of apples selecting them at random, what is the probability that the total weight would exceed 42 pounds? 3.
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