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Name That Distribution! Suppose that milk is shipped to retail outlets in boxes that hold 16 milk containers. One particular box, which happens to contain 6 underweight containers, is opened for inspection, and 5 containers are chosen at random. What is the probability that at least 1 of the 5 selected containers will be underweight? Ans: 0.9423 A traffic control engineer reports that 75% of the vehicles passing through a checkpoint are from within the state. What is the probability that fewer than 2 of the next 5 vehicles are from out of state? Ans: 0.6328 Suppose that a computer programmer, on average, makes 3 errors in 500 lines of code. What is the probability that the programmer will make no errors in 250 lines of code? Ans: 0.2231 There are 70 people in this class. 10 are women. If we form a committee by randomly choosing 5 people, what is the probability that there will be no women on the committee? Ans: 0.4513 Ten is the average number of oil tankers arriving each day at a certain port city. The facilities can handle at most 15 tankers per day. What is the probability that on a given day, tankers will have to be turned away? Ans: 0.0487 If 7 cards are dealt from an ordinary deck of 52 cards, what is the probability that exactly 2 of them will be face cards (ace, king, queen, jack)? Ans: 0.3381 An Air Force intercept squadron consists of 16 planes that should always be ready for immediate launch. However, there is a probability of 0.25 that the engines of a particular plane will not start at a given attempt. If this happens, the mechanics must wait 5 minutes before trying to start the engine again. What is the expected number of planes to immediately launch? Ans: 12 Magnetic tape is slit into half inch widths that are wound into cartridges. A slitter assembly contains 48 blades. Five blades are selected at random and evaluated each day for sharpness. If any dull blades are found the assembly is replaced. If 10 of the blades are dull, what is the probability that the assembly is replaced? Ans: 0.7069 The number of cracks in a section of interstate highway that are significant enough to require repair averages 2 per mile. What is the probability that there will be at least 1 crack in the next ½ mile of highway? Ans: 0.6321 A particularly long traffic light on your morning compute is green 20% of the time that you approach it. Over 20 mornings, what is the probability that the light is green on exactly 4 days? Ans: 0.2182 A small grocery store has 3 check-out counters. The probability that no counters are active on a Saturday morning is 0.05. The probability that 1 counter is active is 0.25. The probability that 2 counters are active is 0.50. What is the expected number of counters to be active on Saturday morning? Ans: 1.85