Furniture manufacturing companies often deal with the quality of the drilling of dowel holes. Consider the case of Company X, 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 6 %. To monitor its drilling process, the company randomly samples products each hour and determines if the dowel hole in each product is correctly drilled or not. If, in the sample of holes, 1 or more incorrectly drilled holes is discovered, the production process is stopped and the drilling process is recalibrated. Use this information to complete parts a through c. a. If the process is really operating correctly (p = 0.08). 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 true detect rate has risen to 0. 10. What is the probability the sample will produce results that property tell the managers to halt to recalibrate the drilling machine?
c. Discuss the effectiveness of the sampling process that the company is using. Base your response on the results to pads a and b.