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?