The manager of an accounting office at a large hospital was interested in studying the problem of errors in the entry of account numbers into the computer system. A group of 200 account numbers was selected from each day's output and each was inspected to determine whether it was incorrect (i.e. a nonconforming item). A total of 155 nonconforming items were found over 25 days.

(a) Calculate the center line and 3-sigma control limits for the p (or np) chart.

(b) Out-of-control signals are also indicated by "at least two out of three consecutive points beyond 2-sigma". Construct also 2-sigma limits.

(c) Suppose there were 10, 10, 13 nonconforming items on the next three consecutive days. Would these observations be unusual?

(d) A new operator had been employed but unknown to the manager her error rate was 0.08. What is the probability that this higher rate will be detected by her third day?