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Unformatted text preview: STAT 410 Practice Problems Fall 2009 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 1 = 1,000, 2 = 500, 3 = 300, 1 = 100, 2 = 80, and 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. A machine fastens plastic screw-on caps onto containers of motor oil. If the machine applies more torque than the cap can withstand, the cap will break. Both the torque applied and the strength of the caps vary. The capping machine torque has the normal distribution with mean 7.9 inch-pounds and standard deviation 0.9 inch-pounds. The cap strength (the torque that would break the cap) has the normal distribution with mean 10 inch-pounds and standard deviation 1.2 inch-pounds. The cap strength and the torque applied by the machine are independent. What is the probability that a cap will break while being fastened by the capping machine?...
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This note was uploaded on 04/15/2010 for the course STAT 410 taught by Professor Monrad during the Fall '08 term at University of Illinois, Urbana Champaign.
- Fall '08