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The Useful Lifetime of a Brand of Automobile Battery Is

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The useful lifetime of a brand of automobile battery is normally distributed with mean 1,100 days and standard deviation 80 days. For how long should these batteries be guaranteed if the manufacturer wants to replace only five percent of the batteries sold because they "died" before the guarantee expired?
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Definitions:

Irrigation System

A network of supplies and managements used to provide water to agricultural land to aid in the growing of crops.

Total Investment

The complete amount of money allocated for the purchase of new assets, expansion of operations, or other investments within a particular period.

Expected Rate Of Return

The projected return on an investment, considering both the probability of gains and the potential for losses, over a specific time period.

Interest Rates

The percentage charged on the total amount of borrowed money, or paid as earnings on an investment.

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