Question: Quick Start Company makes 12-volt car batteries. After many years of product testing, the company knows that the average life of a Quick Start battery is normally distributed, with a mean of 45 months and a standard deviation of 8 months. (a) If Quick Start guarantees a full refund on any battery that fails within the 36~month period after purchase, what percentage of its batteries will the company expect to replace? (b) If Quick Start wish to modify the full refund policy so only 1.5% of its batteries expected to be replaced, for how long (in months) should the company guarantee the batteries?

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