A new water filtration system is sold with a 10-year warranty that includes all parts and repairs. Suppose the life of this water filtration system is normally distributed with mean and standard deviation of 16 and 5 years, respectively.

a. What is the probability that the water iltration system will require a repair during the warranty period?

b. Suppose the water filtration firm makes a $300 profit for every new system it installs. This profit, however, is reduced to $50 if the system requires repair during the warranty period. Find the expected profit of the firm if it installs 1,000 new water filtration systems.