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. The random variable is the age of the dishwasher.

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?