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 .3 year. 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 $ 5 installation charge will be waived.
a. What percentage of batteries would you expect to fail before the warranty period expires?
b. A competitor is offering a warranty of 30 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 30-month warranty on it. How much more would the company have to charge on its “premium” battery to offset the additional cost of replacing batteries?
c. What other factors would you take into consideration besides the price of the battery?