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6. (20 pts) The lifespan of an electrical component is assumed to be normally distributed with an average life of 10 years and a standard deviation of 2 years. The electrical component manufacturer wants to offer their customers a product-replacement guarantee, but hopes to replace at most only 12.3% of the components due to failure. How long of a replacement guarantee period should the manufacturer offer to buyers of this part? (This ones a bit tougher. Partial credit is certainly possible. Hint: you will need to use the Z-score table again.)

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