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The average lifetime of certain type of vehicle is 10 years with a standard deviation of 2 years. To spur on sales, the manufacturer wants

The average lifetime of certain type of vehicle is 10 years with a standard deviation of 2 years. To spur on sales, the manufacturer wants to offer a warranty that will cover all repair or replacement costs on new vehicles for a period of time. If the manufacturer is willing to pay these costs for at most 3% of the cars that fail, for how long should a warranty provide coverage (in years)? Assume the lifetime of a car follows a normal distribution.

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