Points$]$

CAMMBA$411.$E$\mathrm{.}008.$ 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 average cost of the promotion $($in $$)?($Use at least $1,000$ trials. Round your answer to two decimal places.$)$ $

$($b$)$ What is the probability that Grear will refund more than $$25$ for a tire? $($Use at least $1,000$ trials. Round your answer to three decimal places.$)$