A manufacturer calculates that the lifetime of laptop batteries is normally distributed with mean life of 28 months and a standard deviation of 7.5 months. The manufacturer gives a 12-month guarantee on each battery. 1. Use appropriate notation to represent this specific normal distribution 2. What is the probability that a battery will last at least 28 months? 3. What is the probability that a battery will last more than 38 months? 4. What is the probability that a battery will last'less than 12 months? 5. The manufacturer makes 5000 batteries each month. According the normal distribution how many batteries are likely to be returned given the 12-month guarantee? 6. The company CFO thinks that the 12-month guarantee results in too many returns. How should the manufacturer change the guarantee policy that less than 20 batteries will be returned (assume 5000 batteries will be produced monthly)