please answer this question in full 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