For Exercise 9-13, find the C_p index. Comment on the ability of the process to meet specifications. What proportion of the specification range is used up by the process? If it is easier to change the process mean than to change its variability, to what value should the process mean be set to minimize the proportion of nonconforming products?

Exercise 9-13

A pharmaceutical company producing vitamin capsules desires a proportion of calcium content between 40 and 55 ppm. A random sample of 20 capsules chosen from the output yields a sample mean calcium content of 44 ppm with a standard deviation of 3 ppm. Find the natural tolerance limits of the process. If the process is in control at the present values of its parameters, what proportion of the output will be nonconforming, assuming a normal distribution of the characteristic?