A tire companha is developing a new steel-belted radial tire to be sold through a national chain of discount stores.

A tire companha is developing a new steel-belted radial tire to be sold through a national chain of discount stores. Before finalizing the tire mileage guarantee policy, the managers want probability information about X= the number of miles the tires will last. From actual road tests with the tires, it is estimated that the true mean tire mileage is 36,500 and the standard deviation id 5000 miles. In addition, the collected data indicate the a normal distribution is a reasonable assumption.

a) what percentage of the tires can be expected to last more than 40,000 miles?

b) what should the guaranteed mileage be if the company wants no more than 10% of the tires to be eligible for the discount guarantee?

c) find the probability that in the first group of 12 tires sold, more than one tire will fall into the guarantee.