Question: A tire company has invented a revolutionary new product. In order to overcome consumer resistance a mileage guarantee is offered with the tire. Road tests suggest that the mean life of the tire is 42,000 miles, with a standard deviation of 4,000 miles. The tests suggest that tire life is normally distributed.

(a) What percentage of tires will last for more than 45,000 miles?

(b) What should the guaranteed mileage be if the firm wishes to replace no more than 4 per cent of tires?