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For a new type of​ tire, a racing car team found the average distance a set...

For a new type of​ tire, a racing car team found the average distance a set of tires would run during a race is 166 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 _  miles.

The standard deviation for miles remaining is _ miles.

​b) The probability they​ won't have to change tires a third time is _

Math   Statistics-And-Probability   
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