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Exercises on Discrete distributions 1 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? 2 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? 3 Six is the average number of oil tankers arriving each day at a certain port city. The facilities can handle at most 10 tankers per day. What is the probability that on a given day, some tankers will have to be turned away? 4 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 engine of each 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? 5 The number of cracks in a section of interstate highway averages 2 per mile. What is the probability that there will be at least 1 crack in the next ½ mile of the highway? 6 A particularly long traffic light on your way to work in the morning 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? 7