please answer questions 8 and 6 in full please this is mgmt science operations mgmt section 01.

5) [20 points] A tire manufacturer has been concerned about the number of defective tires found recently. In order to evaluate the true magnitude of the problem, a production manager selected 20 random samples of 50 units each for inspection. The number of defective tires found in each sample are as follows: a) Calculate the p-bar, standard deviation, upper and lower control limits. Show all calculations. (You may use Excel tools to verify your answers). b) Plot the p-chart. (You may use Excel tools to plot the charts.) c) Based on the p-chart, discuss whether the process in statistical control or not. [10 points] Three ice-cream packing machines at the Creamy Treat Company are being evaluated for their capability. If design specification of the ice-cream packing process is 16.000.20 ounces. The following data is recorded. a) Compute the process capability indexes Cp,Cpl,Cpu, and Cpk for each machine. b) Which machines are capable of achieving four-sigma performance (the four-sigma performance target value is 1.33 )