Adishwasher has a mean life of 12 years with an estimated standard deviation of 1.25 years ("appliance life expectancy," 2013). assume the life of a dishwasher is normally distributed. a.) state the random variable. a. b.) find the probability that a dishwasher will last more than 15 years. c.) find the probability that a dishwasher will last less than 6 years. d.) find the probability that a dishwasher will last between 8 and 10 years. e.) if you found a dishwasher that lasted less than 6 years, would you think that you have a problem with the manufacturing process? why or why not? f.) a manufacturer of dishwashers only wants to replace free of charge 5% of all dishwashers. how long should the manufacturer make the warranty period?