Appraoching the third year of the COVID-19 pandemic, new variants are emerging forcing individuals, families, communities and nations to continue adhereing to stringent protocols, particularly the wearing of masks in public spaces. A mask manufacturing company, recognising the critical role good quality masks play in helping to prevent the spread of the virus, has adopted a strict quality management programme to ensure the masks produced coform to specified standards. This requires inspecting samples from each batch of masks produced for conformance to specifications Table 1 shows the number of non-conforming masks in samples of size 100 pulled from 20 batches. Construct a fraction non-conforming (p) chart for this data set. Table 1. Number of non-conforming masks in samples of 100 from 20 batches Sample Number Number of Non-conforming Masks 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 7 4 1 3 6 8 10 5 2 7 6 15 0 9 5 1 4 5 7 12 A defective mask is considered to be one that is incorrectly sized, made of wrong materials or snaps when stretched. As a Quality Management intern employed with this organization, management has supplied you with this data and assigned you the task of making suitable recommendations. You proceeded with the following three steps: (6 marks) a) Calculate the control limits necessary for constructing a p-chart. Show all calculations in your response. (5 marks) b) Construct a p-chart to represent the data. (include a table clearly showing the data used to construct the chart) c) What control limits will you recommend for future data? (5 marks) d) Assuming assignable causes for the phenomenon observed in part (c). propose two suitable actions management could take to reduce the number of defective masks produced. (4 marks)