a pharmaceutical company producing vitamin capsules desires a proportion of calcium content between 40 and 50ppm. a random sample of 20 capsules chosen from the output yields a sample mean calcium content of 44ppm 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?

then find the Cpk index and comment on process peformance.

if the target value is 47.5ppm, find the Cpm and Cpmk indices and comment on their values.