For a new type of tire, a racing car team found the average distance a set of tires would run during a race is 160 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? a) The expected value for miles remaining is 180 miles. (Type an integer or decimal rounded to three decimal places as needed.) The standard deviation for miles remaining is 16.971 miles (Type an integer or decimal rounded to three decimal places as needed.) b) The probability they won't have to change tires a third time is (Type an integer or decimal rounded to three decimal places as needed.)