A Maytag dishwasher has a mean life of 12 years with an estimated standard deviation of 1.25 years. Assume the life of a dishwasher is normally distributed.

A Maytag dishwasher has a mean life of 12 years with an estimated standard deviation of 1.25 years.  Assume the life of a dishwasher is normally distributed.

(a) What is 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) Maytag only wants to replace free of charge 5% of all dishwashers.  How long should the manufacturer make the warranty period?

Continuing with this problem, suppose now a sample of 10 dishwashers are chosen from the above normal distribution.

(g) Describe the distribution of the sample means: What is its shape? What is its mean? What is its standard deviation?

(h) Find the probability that the sample mean of the dishwashers is less than 6 years.

(i) If you found the sample mean life of the 10 dishwashers to be less than 6 years, would you think that you have a problem with the manufacturing process?   Why or why not?