The city parks chief is concerned about sprinkler systems corroding in parks and failing to operate. Using a sample of 100 sprinklers in operation the previous year, the parks department regresses whether a sprinkler failed (Y coded 1 for failure and 0 for no failure) on the age of the sprinkler system. The department gets the following regression equation (X is age in years):
 = .06 + .016Xsb = .0006
Sy|x = .04r2 = .56
(a) Is there a relationship between corrosion and sprinkler failure?
(b) The sprinkler system in Frolic Park is 52 years old. What is the probability that this sprinkler system will fail?
(c) A sprinkler system that is only 2 years old fails in Barren Park. What is the probability that this will happen?
(d) What is the probability that the 65-year-old sprinkler system in Choirpractice Park will fail?