Grear Tire Company has produced a new tire with an estimated mean lifetime mileage of 33,500 miles. Management also believes that the standard deviation is 4,500 miles and that tire mileage is normally distributed. To promote the new tire, Grear has offered to refund a portion of the purchase price 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. Construct a simulation model to answer the following questions. (Use at least 1,000 trials.)

(a)

For each tire sold, what is the average cost of the promotion (in $)? (Round your answer to two decimal places.)

$

(b)

What is the probability that Grear will refund more than $25 for a tire? (Round your answer to three decimal places.)