The Grear Tire Company

1
The Grear Tire Company

• Problem

2
A Business Application

• Suppose that the Grear Tire Company has just
  developed a new steel-belted tire that will be
  sold through a national chain of discount stores.
  Grears 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,
  Grears management would like some probability
  information concerning the number of miles the
  tires will last.

3
Grear Tire Problem

• From actual road tests with tires, Grears
  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.

4
Grear 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??

5
Grear Tire Problem

• Let us assume that Grear 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 Grear
  would like no more than 10 of the tires to be
  eligible for the discount guarantee?