Grear Tyre Company has just developed a new steel-belted radial tyre that will
be sold through a national chain of discount stores. Because the tyre is a new
product, the company’s management believes that the mileage guarantee
offered with the tyre will be an important factor in the consumer acceptance of
the product. Before finalizing the tyre mileage guarantee policy, the actual road

test with the tyres shows that the mean tyre mileage is μ = 36,500 kilometres
and the standard deviation is σ = 5,000 kilometres. In addition, the data
collected indicate that a normal distribution is a reasonable assumption.
Required:
(i) Grear Tyre Company will distribute the tyres if 20 per cent of the tyres
manufactured can be expected to last more than 40,000 kilometres.
Should the company distribute the tyres?
(4 marks)
(ii) The company will provide a discount on a new set of tyres if the mileage
on the original tyres does not exceed the mileage stated on the guarantee.
What should the guarantee mileage be if the company wants no more
than 10% of the tyres to be eligible for the discount? (4
marks)