Question: The city parks chief is concerned about sprinkler systems corroding in parks and failing to operate. Using a sample of 100 sprinklers in operation and previous year, the parks department regresses whether a sprinkler failed (Y, coded 1 fore 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);

Y = .06 + .0166X sb=.0006 Sy/x = .04 r2 = .56

A Is there a relationship?

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 Choir Practice Park will fail?