Question: A manufacturer of tires has found that the lifetime of a certain kind of tire is a normally distributed random variable with a mean of 30,000 miles and standard deviation 2,000 miles. The company wishes to guarantee it for N miles with a full refund if the tire does not last that long. Suppose it wants to make sure that the probability that a tire will be returned is no more than 0.10 (that is, no more than 10 percent of the tires sold will be returned). What value of N should the company choose?