Grear Tire Company has produced a new tire with an estimated mean lifetime mileage of 36,500 miles. Management also believes that the standard deviation is 5,000 miles and
that tire mileage is normally distributed. To promote the new tire, Grear has offered to
refund some money if the tire fails to reach 30,000 miles before the tire needs to be
replaced. Specifically, for tires with a lifetime below 30,000 miles, Grear will refund a
customer $1 per 100 miles short of 30,000.
a) For each tire sold, what is the expected cost of the promotion?