4. The normal distribution An automobile battery manufacturer offers a 39/50 warranty on its batteries. The...

4. The normal distribution An automobile battery manufacturer offers a 39/50 warranty on its batteries. The first number in the warranty code is the free-replacement period; the second number is the prorated-credit period. Under this warranty, if a battery fails within 39 months of purchase, the manufacturer replaces the battery at no charge to the consumer. If the battery fails after 39 months but within 50 months, the manufacturer provides a prorated credit toward the purchase of a new battery. The manufacturer assumes that x, the lifetime of its auto batteries, is normally distributed with a mean of 44 months and a standard deviation of 3.6 months. Use the following Distributions tool to help you answer the questions that follow. (Hint: When you adjust the parameters of a distribution, you must reposition the vertical line (or lines) for the correct areas to be displayed.) If the manufacturer’s assumptions are correct, it would need to replace of its batteries free of charge. The company finds that it is replacing 9.34% of its batteries free of charge. It suspects that its assumption about the standard deviation of the life of its batteries is incorrect. A standard deviation of results in a 9.34% replacement rate. Using the revised standard deviation for battery life, what percentage of the manufacturer’s batteries don’t qualify for free replacement but do qualify for the prorated credit? 40.66% 5.71% 84.95% 44.29%

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orchestra answered 2 years ago

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