Tim the tire dealer wants to set the warranty on a particular brand of tires so

Question

Tim the tire dealer wants to set the warranty on a particular brand of tires so that 15% of the customers, at most, return tires because of premature wear. Tim obtains the following representative data on the life span of a sample of tires from some of his customers (mileage rounded to the nearest mile). What mileage should Tim guarantee in his warranty? (Round your answer to the nearest thousand miles.)

a. 16,000 mi

b. 18,000 mi    

c. 21,000 mi

d. 19,000 mi

e. 17,000 mi

15,483 17,759 24,313 27,210 15,595 18,957 24,417 27,964 16,507 21,008 25,775 28,490 17,493 21,812 26,158 29,233 17,531 23,809 26,241 33,578

Explanation / Answer

So here 20 customers data available.

Now Tim wants that only 15% of these customers should return the tires. It means only 15% customers are type of those customers whom Tim guarantee in his warranty.

So we have to find nearest guarantee.

For this we have to calculate 15% customers from collected sample and see what is maximum life span among them.

Here are 20 customers.

15% = (20)×(15/100) = 3

And life span of first three customers are - 15483, 15595, 16507 (all in mi).

So here max is 16507 mi. So Tim should guarantee above this and less than fourth one which life span is 17493.

So overall answer is between 16507 and 17493.

And in nearest thousand miles = 17,000 mi

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