please write out steps, I am actually trying to learn how to perform the functions to solve the problem

(a) A bottle-filling process has a low specification limit of 1.8 liter and upper specification limit of 2.2 liter. The standard deviation is 0.15 liter, and the mean is 2 liter. The company now wants to reduce its defect probability as 0.0455. To what level would it have to reduce the standard deviation in the process to meet this target (you can use Excel spreadsheet or Table 9.1 in the textbook) (30/100 pts)? (b) For 10 consecutive days, a process engineer has measured the temperature of water bottles as they are made ready for serving. Each day, she took a sample of 9 bottles. The average across all 90 bottles (10 days, 9 bottles per day) was 45 degrees Fahrenheit. The standard deviation across all bottles was 1.8 degree. When constructing an X-bar chart, what would be the center line, upper control limit and lower control limit (30/100 pts)? (c) Please draw a Pareto diagram for the situation below (40/100 pts). - Situation: when they ship out tires from their warehouses, they have shipping discrepancy such as tire shortage, tire overage, and tire damage. A lot of non-value-added work is needed to handle the shipping discrepancy. So, they want to find out root causes and eliminate them immediately. - Observations: through brainstorming sessions, they have found possible main causes and root causes of the process. They collected the data and illustrated frequencies of each possible root causes as shown in the table below. Main causes Transportation Jos tires in carriers terminal Root causes stolen during transport Miscounting Leading - miscounted by Warehouse - damaged at loading supervisor no system adjustment - miscounted by customer after loading Wrong Material shipped out wrong patter of tire -shipped out wrong product code of tire Root causes Frequency lost tires in carrier's terminal shipped out wrong pattern of tire miscounted by customer miscounted by warehouse supervisor damaged at loading no system adjustment after loading Nolen during transport whipped out wrong product code of tire . ===