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The X Tire Company Problem

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A Business Application Suppose that the X Tire Company has just developed a new steel-belted tire that will be sold through a national chain of discount stores. X’s management believes that the mileage guarantee offered with tire will be an important factor in the acceptance of the product. Before finalizing the tire mileage guarantee policy, X’s management would like some probability information concerning the number of miles the tires will last.

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X Tire Problem From actual road tests with tires, X’s engineering group has estimated the mean tire mileage at 36,500 miles and the standard deviation at 5000 miles. In addition the data collected indicate that a normal distribution is a reasonable assumption.

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X Tire Problem Using the normal distribution, what percentage of the tires can be expected to last more than 40,000 miles? In other words, what is the probability that the tire mileage will exceed 40,000 miles??

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X Tire Problem Let us assume that X is considering a guarantee that will provide a discount on an new set of tires if the original tires do not exceed the mileage stated in the guarantee. What should the guarantee mileage be if X would like no more than 10% of the tires to be eligible for the discount guarantee?

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Example A population has a mean of 200 and a standard deviation of 50. A random sample of size 100 will be taken and the sample mean x̄ will be used to.

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