A robot that shapes metal needs overhauling if it is out of tolerance on 4.5% of the items processed, and it is operating satisfactorily if it is off on only 0.8% of its output. A test is performed involving 50 sample items.
If the sample proportion of out-of-tolerance items is greater than 0.02, the robot will be overhauled. Otherwise, it will be allowed to continue operating. (a) What is the probability that a satisfactory robot will be overhauled unnecessarily? (b) What is the probability that a robot in need of overhauling will be left in operation?