Question 3. A tire manufacturer warranties its tires to last at least 20,000 miles or “you get a new set of tires.” In its experience, a set of these tires lasts on average 26,000 miles with a standard deviation of 5,000 miles. Assume that the wear is normally distributed. The manufacturer profits $200 on each set sold, and replacing a set costs the manufacturer $400.

(a) What is the probability that a set of tires wears out before 20,000 miles?