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Unformatted text preview: 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 "10pound" 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 "3pound" 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 boyscout troop is planning a camping trip. If the boyscouts buy 3 "10pound" sacks of potatoes and 4 "3pound" bags of apples selecting them at random, what is the probability that the total weight would exceed 42 pounds? 3. Suppose that company A and company B are in the same industry sector, and the prices of their stocks, $X per share for company A and $Y per share for company B, vary from day to day randomly according to a bivariate normal distribution with parameters μ X = 45, σ X...
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This note was uploaded on 02/11/2011 for the course STAT 410 taught by Professor Monrad during the Spring '08 term at University of Illinois, Urbana Champaign.
 Spring '08
 Monrad

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