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 standard deviation 6,000 miles. Assume
that the wear is normally distributed. The manufacturer profits $200 on each set sold, and replacing a set
costs the manufacturer $400.
1.What it the probability that a set of tires wears out before 20,000 miles?
(ii) What is the probability that a set of tires will last for at least 41,000miles?
3.If the manufacturer sells 500 sets of tires, what is his expected profit? Assume that the
purchases are made around the country and that the drivers experience independent amounts of
wear.
(iv) The manufacturer, after calculating the expected profit from selling 500 sets of tires,
decides that he is not happy with his profit and would like to modify the promotion so that his
expected profit increases to $75,000. How should he modify the promotion? In other words,
complete the new promotion line “tires to last at least ….. miles or you get a new set of tires” Again,
assume that the purchases are made around the country and that the drivers experience
independent amounts of wear.