SOLUTION: This question was previously answered incorrectly. Please help me: Suppose the life of a certain brand of vacuum cleaner is normally distributed with a mean life of 12 years and

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Question 446146: This question was previously answered incorrectly. Please help me:
Suppose the life of a certain brand of vacuum cleaner is normally distributed with a mean life of 12 years and a standard deviation of 4 years. A vacuum cleaner is randomly chosen.
10. For how many years should the manufacturer warranty its vacuum cleaners if it is willing to replace only 1% of the vacuum cleaners it sells (Round answer to the closest whole number).
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
Suppose the life of a certain brand of vacuum cleaner is normally distributed with a mean life of 12 years and a standard deviation of 4 years. A vacuum cleaner is randomly chosen.
10. For how many years should the manufacturer warranty its vacuum cleaners if it is willing to replace only 1% of the vacuum cleaners it sells (Round answer to the closest whole number).
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I have rethought the problem to see why the answer would be 21 years.
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50% of the cleaners will last 12 years.
99% of the cleaners will last x = 2.3263*4+12 = 21.3 years
That leaves 1% that will last even longer than 21.3 years.
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Now looking at the failure rate: 50% will fail by 12 years.
As you get beyond 12 years a higher percentage will have failed.
By the time you get to 21.3 years only 1% will not have failed.
If you warrantee the cleaners for 21.3 years you will have to
replace 99% of them; only 1% will still be operating.
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Those are my thoughts. What do you think?
Cheers,
Stan H.