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.) True or False: The random variable x defines the life expectancy of a 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 8 years.
d.) Find the probability that a dishwasher will last between 8 and 10 years.
e.) A manufacturer of dishwashers only wants to replace free of charge 5% of all dishwashers. How long should the manufacturer make the warranty period?