Please hand write your work. Thank you

A bottling machine is designed to fill 16.90 fluid ounces of water in each bottle. However, the actual fillings vary by small quantities. For many reasons, either too much water or too little water per filling is not desirable. Thus, the quality assurance manager puts out the following specification limits for the water content of each bottle: an LSL of 16.81 fluid ounces and a USL of 16.99 fluid ounces. Based on a very large sample of filled bottles, the manager sees that the fillings follow a normal distribution with = 16.93 fluid ounces and = 0.031 fluid ounces. (a)[2] Draw a normal distribution with specification limits to indicate the probabilities of defect. (b)[2] Calculate the probability of defect when too little water is filled in a bottle. (7 decimals) (c)[2] Calculate the probability of defect when too much water is filled in a bottle. (7 decimals) (d)[1] Calculate the probability of defect (DP) when a bottle is filled. Calculate & interpret the DPMO (2 decimal places). (e)[3] Calculate and make a subjective statement about the sigma level (2 decimals) of this bottling machine. Sketch the sigma level. Hint: in Excel, sigma level = Norm.S.Inv(1-DP) + 1.5.