The Lower Tolerance Limit (LTL) and Upper Tolerance Limit (UTL) for the process are, The process capability index is (Cpk), What is the probability of producing defective bottles (outside the tolerance limits)? (Carry 3 decimals, ex: 0.057 or 5.7%) and Suppose the process is re-centered and the new sample mean is 200 milliliters. What is the maximum variability (standard deviation) the process can have if the company wants to have Cpk = 1.25?

A small start-up business claims to have develop the best hydration and energy replacement drink for professional soccer. Their drink, called "HE2", is known to have purified water, sodium, potassium, chloride, protein, and other elements (all kept as trade secret, thus not even applying for a patent) seems to be the favorite drink of teams like, Barcelona, Real Madrid, PSG, and France - the 2018 world cup champions. The firm's specifications require that the amount in each bottle should be 200 milliliters, + 3 milliliters. An operator randomly takes several sample measurements at scheduled intervals. The most recent measurements show that the sample mean is 201 milliliters with a standard deviation of 1.1 milliliters. (There are four questions based on this data)