Question: A device has an average life of 2.7 years. This is distributed normally with a standard deviation of 0.3 years. The devices are warranted to operate for 2 years. If the device fails inside the warranty period, it will be replaced at no charge, and the $50 installation charge will be waived.
a. What percentage of batteries would be expected to fail within the warranty period?
b. The marketing office is considering introducing a "premium" device, which is exactly the same as the current device but with a fancy coat of paint and a 30-month warranty. How much would the company need to charge for the "premium" device to offset the cost of additional replacements?