A certain type of refrigerator has a length of life that is approximately normally distributed with a mean of 4.8 years and a standard deviation of 1.3 years.

a. If this machine is guaranteed for 2 years, what is the probability that the machine you purchased will require replacement under the guarantee?

b. What period of time should the manufacturer give as a guarantee if it is willing to replace only 0.5% of the machines?