Answer to Question #31929 in Statistics and Probability for kharisma

Question

1. In a manufacturing process 15 units are randomly selected each day from the production line to check the percent defective of the process. From historical information it is known that the probability of a defective unit is 0.05. Any time that two or more defectives are found in the sample of 15, the process is stopped. This procedure is used to provide a signal in case the probability of a defective has increase.
a. What is the probability that on any given day the production process will be stopped? (Assume 5% defective.)
b. Suppose that the probability of a defective has increased to 0.07. What is the probability that on any given day the production process will not be stopped?