For a new type oftire, a racing car team found the average distance a set of tires would run during a race is 161 miles, with a standard deviation of 14 miles. Assume that tire mileage is independent and follows a Normal model.

a) If the team plans to change tires twice during a500-mile race, what is the expected value and standard deviation of miles remaining after twochanges?

b) What is the probability theywon't have to change tires a third time(and use a fourth set oftires) before the end of a 500 milerace?

Please answer both parts of the question, thank you!