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Auto batteries have an average life of 2 . 7 years. Battery life is normally distributed with a mean of 2 . 7 years and

Auto batteries have an average life of 2.7 years. Battery life is normally distributed with a mean of 2.7 years and a standard deviation of 0.4 years. The batteries are warranted to operate for a minimum of 2 years. If a battery fails within the warranty period, it will be replaced with a new battery at no charge. The company sells and installs the batteries. Also, the usual $3 installation charge will be waived.
Use and Table B.
a. What percentage of batteries would you expect to fail before the warranty period expires? (Round your z value to 2 decimal places. Round probabilities to 4 decimal places. Round your final answer to 2 decimal places.)
b. A competitor is offering a warranty of 31 months on its premium battery. The manager of this company is toying with the idea of using the same battery with a different exterior, labeling it as a premium battery, and offering a 31-month warranty on it. What percentage of the batteries would you expect to fail before this new warranty period expires? (Round your z value to 2 decimal places. Round probabilities to 4 decimal places. Round your final answer to 2 decimal places.)

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