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For a new type of? tire, a racing car team found the average distance a set of tires would run during a race is 167 ?miles, with a standard deviation of 12 miles. Assume that tire mileage is independent and follows a Normal model.
?a) If the team plans to change tires twice during a? 500-mile race, what is the expected value and standard deviation of miles remaining after two? changes?
?b) What is the probability they? won't have to change tires a third time? (and use a fourth set of? tires) before the end of a 500 mile? race?
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