A tire company has developed a new type of steel-belted radial tire. Extensive testing indicates that the population of mileages obtained by all tires of this type are normally distributed with a mean of 60,000 kilometres and a standard deviation of 2,000 kilometres. The automobile company would like to test whether the manufacturing process was working correctly for the shipment of tires they received - i.e. they want to test whether the mean life of the tires they received is 60,000 kilometres. To test this the auto company will test the durability of a sample of tires, estimating the sample mean. They would like to take a large enough sample to create a 95% confidence interval for the mean tire life that is no wider than 500 kilometres. How large a sample of tires should the company test?