a tire manufacturer warranties its tires to last at least 20,000 miles or "you get a new set". In its experience, a set of these tires last 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 ?
B) what is the probability that the manufacturer turns a profit on selling a set to one customer.
C) if the manufacturer sells 500 sets of tires, what is the probability that it earns a profit after paying for any replacements? Assume that the purchases are made around the country and that the drivers experience independant of the amount of wear.