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Question 4 (25 pts) The speed of vehicles along a stretch of road is described by a random variable V which has a normal distribution with mean of 75 kph (kilometer per hour) and standard deviation of 10 kph. a. A vehicle is selected randomly, what is the probability that is speed is between 70 kph to 80kph. (5pt) b. The current speed limit is 80 kph. What is the probability that the speed of a randomly selected vehicle is over the speed limit. (5pt) c. Knowing that a randomly selected vehicle has speed higher than 60 kph, determine the probability that the speed of the vehicle is over the speed limit? (7pt) d. Five independent vehicles are selected randomly, what is the probability that at most one of them is over the speed limit? (8pt)
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