Triple A Battery Company is a majorbattery manufacturer of batteries and it produces three types ofbatteries (Type A, B, and C). The batteries are similar inconstruction but carry a different warranty period. Type A has a 36month warranty, Type B has a 48 month warranty, and Type C has a 60month warranty. Regardless of the warranty period, the standarddeviation of a battery’s life is 2.5 months. Let’s consider the 36month battery (Type A) for the following questions.

1. If the average life of a Type A battery is 38 months, then whatproportion of the batteries will fail before the warrantyperiod?
2. If a Type A battery is chosen at random, what is theprobability that battery will last at least 42 months? Assume themean life time of the battery is 38 months.
3. Each year, the company establishes a budget for warranty costs.If a battery does not last until the warranty period expires, thenthey have to replace the battery at no charge to the customer. Thisyear they expect to replace 2% of the Type A batteries. What is thecutoff point, in months, for this 2%?
4. Given the scenario in the previous problem, what would the meanlifetime have to be for the company to stay under budget for theType A batteries? In other words, what would the mean have to be ifonly 2% of the population is less than 36 months?
5. The company has found that if their Type A batteries last atleast 6 months beyond the warranty period (44 months or more), thenthe customer is sure to buy their battery as a replacement when itfails. What portion of the customers can they count on as beingrepeat customers? Assume the mean life is 38 months.