For the AX-527 tire model, rubber exits the extruder at a rate equivalent to 10,000 tires per hour. The output must therefore meet specific tolerance standards. In particular, the thickness should be 400 10 thou (1 thou = 0.001 inch). Susanne and her team analyzed several output samples from the extruder and determined that if its settings were correct, the thickness of the output produced by the extruder, X, would follow a normal distribution with a mean of 400 and a deviation kind of 4.

1: If the parameters were correct, what proportion of the production would meet the tolerance standards?

2. Calculate the Cp value.

3. When one of its bearings starts to deteriorate, the extruder produces sheets with an average thickness of 403, despite the setting being set at 400. This is not visible to the naked eye. In this situation, what proportion of sheets will be defective?

4. Suppose further that the process mean has drifted towards 403. If one were to operate with the process control limits already set at [396.2, 403.8], what would be the probability that a sample size n = 10 signals that the process is in control failure?