Question: In his article titled "Acceptance Sampling Solves Drilling Issues: A Case Study," published in Woodworking Magazine, author Ken Wong discusses a problem faced by furniture manufacturing companies dealing with the quality of the drilling of dowel holes. Wong states, "Incorrect sizing and distances with respect to dowel holes can cause many problems for the rest of the process especially when drilling is conducted early in the production process." Consider the case of Dragon Wood Furniture in Bismarck, North Dakota, which believes that when the drilling process is operating at an acceptable rate, the upper limit on the percentage of incorrectly drilled dowel holes is 4%. To monitor its drilling process, Dragon Wood Furniture randomly samples 20 products each hour and determines if the dowel hole in each product is correctly drilled or not. If, in the sample of 20 holes, 1 or more incorrectly drilled holes is discovered, the production process is stopped and the drilling process is recalibrated.

a. If the process is really operating correctly (p = 0.042), what is the probability that the sampling effort will produce x = 0 defective holes and thus the process will properly be left to continue running?

b. Suppose the true defect rate has risen to 0.10. What is the probability the sample will produce results that properly tell the managers to halt production to recalibrate the drilling machine?

c. Prepare a short letter to the manufacturing manager at Dragon Wood Furniture discussing the effectiveness of the sampling process that her company is using. Base your response on the results to parts a and b.