As the supervisor in charge of shipping and receiving, you need to determine the average outgoing quality in a plant where the known incoming lots from your assembly line have an average defective rate of $3.0 \%$. Your plan is to sample 80 units of every 1,000 in a lot. The number of defects in a sample is not to exceed 3 . Such a plan provides you with a probability of acceptance of each lot of $0.79(79 \%)$.
The average outgoing quality for the plant is $=\square \%$ (enter your response as a percentage rounded to two decimal places).
Answer
To determine the average outgoing quality, we need to consider the average defective rate and the probability of acceptance of each lot. The average defective rate is 3.0%, which means that out of every 1000 units, 30 are defective. The plan is to sample 80 units of every 1000 in a lot, and the number of defects in a sample is not to exceed 3. This plan provides a probability of acceptance of each lot of 79%. Therefore, the average outgoing quality is the product of the average defective rate and the probability of acceptance. Average Outgoing Quality = Average Defective Rate * Probability of Acceptance = 3.0% * 79% = 2.37% So, the average outgoing quality for the plant is 2.37%.
Step 1 ：To determine the average outgoing quality, we need to consider the average defective rate and the probability of acceptance of each lot. The average defective rate is 3.0%, which means that out of every 1000 units, 30 are defective. The plan is to sample 80 units of every 1000 in a lot, and the number of defects in a sample is not to exceed 3. This plan provides a probability of acceptance of each lot of 79%. Therefore, the average outgoing quality is the product of the average defective rate and the probability of acceptance. Average Outgoing Quality = Average Defective Rate * Probability of Acceptance = 3.0% * 79% = 2.37% So, the average outgoing quality for the plant is 2.37%.
