In past, n = 50 fuses are tested each hour and pbar = 0.03 have been defective. Compute the UCL and LCL. After the production error, assume that true p shifts to p = 0.05.
(a) Determine the probability that the next observation exceed the UCL?
(b) Determine the probability that at least one of the next five observations exceeds the UCL.
Hint: Suppose independence and compute the probability that none of the next five exceeds the UCL.