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 3ppm. (a) Find the natural tolerance limits of the process. (b) 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? (c) Find the PCR index. Comment on the ability of the process to meet specications. (d) What proportion of the specication range is used up by the process? (e) 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 product? Has it improved relative to the present setting of the process mean? (f) Find the PCRk and commnet on process performance. If the target value is 47.5ppm. Find PCRkm and commnet on its value.