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Solved: In a chemical processing plant, it is important
Chapter 6, Problem 6.67(choose chapter or problem)
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 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 batch will have a yield that exceeds 80% when in fact the mean yield is 79%?
Questions & Answers
QUESTION:
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 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 batch will have a yield that exceeds 80% when in fact the mean yield is 79%?
ANSWER:Q: In a chemical processing plant, it is important that the yield of a certain type of batch productstay above 80%. If it stays below 80% for an extended period of time, the company loses money.Occasional defective 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 distributedwith standard deviation 4%. (a) What is the probability of a false alarm (yield below 80%) whenthe mean yield is 85% (b) What is the probability that a batch will have a yield that exceeds80% when in fact the mean yield is 79% Step By Step SolutionStep 1of 2:(a)Given:Mean:Standard deviation:False alarm arises if yield is below 80%, therefore:Therefore the probability of a false alarm is 0.1056.