4) 6.3.8 A dishwasher 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. 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? 5) 6.3.10 The