In a chemical processing plant it is important that the yield of a certain type of batch product stay above 80%. If it stays below 80% for an extended period of time, the company loses money. Occasional defective manufactured batches are of little concern. But if several batches per day are defective, the plant shuts down and adjustments are made. It is known that the yield is normally distributed with standard deviation 4%.
a) What is the probability of a "false alarm" (yield below 80%) when the mean yield is 85%?
b) What is the probability that a manufactured batch will have a yield that exceeds 80% when in fact the mean yield is 79%?