SOLUTION: From actual road tests with the tires, Hankook Tires estimated that the mean tire mileage is 36,500 miles and that the standard deviation is 5000 miles. Data is normally distribute

Question 1183574: From actual road tests with the tires, Hankook Tires estimated that the mean tire mileage is 36,500 miles and that the standard deviation is 5000 miles. Data is normally distributed.
(i) What percentage of the tires can be expected to last more than 40,000 miles?
(ii) Assume that Hankook Tires is considering a guarantee that will provide a discount on replacement tires if the original tires do not provide the guaranteed mileage. What should the guarantee mileage be if the company wants no more than 10% of the tires to be eligible for the discount guarantee?

Found 2 solutions by Boreal, ikleyn:
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
z>(40000-36500)/5000=0.7
That probability is 0.2420 or 24.2%
-
The 10th percentile of this distribution has z=-1.282
-1.282=(x-36500)/5000
-6410=x-36500
x=30090 miles
Answer by ikleyn(52776) (Show Source): You can put this solution on YOUR website!
.
From actual road tests with the tires, Hankook Tires estimated that the mean tire mileage is 36,500 miles
and that the standard deviation is 5000 miles. Data is normally distributed.
(i) What percentage of the tires can be expected to last more than 40,000 miles?
(ii) Assume that Hankook Tires is considering a guarantee that will provide a discount on replacement tires
if the original tires do not provide the guaranteed mileage. What should the guarantee mileage be
if the company wants no more than 10% of the tires to be eligible for the discount guarantee?
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I think that the basic assumption made in this problem that the tire mileage is described by the normal distribution

is INCORRECT and CONTRADICTS to COMMON SENSE, as well as to the MATERIAL SCIENCE.

THEREFORE, I think, the problem, as it is worded, printed, posted and presented, is a FAKE.

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It is the same as to assume that the age of people is distributed normally, which is, OBVIOUSLY, not a case.

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