3. A soft-drink bottle filling facility has been operating in the region PIKE for the past three decades. Recently, the facility replaced the existing filling systems with new systems. While the contractor firm who was responsible for the replacement project promised the machine will be functioning "really really well", the firm needed to know more about the characteristics of the process. There were total two machines replaced. The process characteristics study data are provided in a separate Excel spreadsheet. Their primary customer is looking for the following specifications: 16.9 +0.18 a. Please analyze each column of dala separately. Please construct the histograms for each column to discuss what is the mean, standard deviation, and the shape of the distribution. Hint: one of the machines is operating more like a uniform distribution. In case of a uniform distribution, its mean is (max + min), the variance is (max - min) b. What is the DPMO if the sample results are very good representation of the actual working condition? For one of the machines that assumes the normal distribution, please identify the Cpk. (hint: specifications are provided in the description) c. Assuming the loss function constant is k = 8, which machine will generate a greater loss? d. Do you find the answers from question band c telling the consistent story about the machine and their quality outcome? If yes, why? If no, how can you reconciliate the contradiction? 3. A soft-drink bottle filling facility has been operating in the region PIKE for the past three decades. Recently, the facility replaced the existing filling systems with new systems. While the contractor firm who was responsible for the replacement project promised the machine will be functioning "really really well", the firm needed to know more about the characteristics of the process. There were total two machines replaced. The process characteristics study data are provided in a separate Excel spreadsheet. Their primary customer is looking for the following specifications: 16.9 +0.18 a. Please analyze each column of dala separately. Please construct the histograms for each column to discuss what is the mean, standard deviation, and the shape of the distribution. Hint: one of the machines is operating more like a uniform distribution. In case of a uniform distribution, its mean is (max + min), the variance is (max - min) b. What is the DPMO if the sample results are very good representation of the actual working condition? For one of the machines that assumes the normal distribution, please identify the Cpk. (hint: specifications are provided in the description) c. Assuming the loss function constant is k = 8, which machine will generate a greater loss? d. Do you find the answers from question band c telling the consistent story about the machine and their quality outcome? If yes, why? If no, how can you reconciliate the contradiction