PLEASE SOLVE THE QUESTION WITHOUT USING EXCEL

Q8. The Great Outdoors Clothing Company, a mail-order catalogue operation, contracts with the Federal Parcel Service to deliver all of its orders to customers. Great Outdoors processes orders rapidly and requires Federal Parcel to pick them up and deliver them rapidly. Great Outdoors has tracked the delivery time for five randomly selected orders for 12 samples. Samples 1 2 2 5 4 3 4 6 5 2 5 6 7 8 9 10 11 12 Delivery Time (days) 3 3 4 3 3 6 2 1 3 3 2 2 1 5 3 3 4 1 4 4 1 3 3 3 3 3 2 1 1 3 2 2 3 3 3 3 7 5 5 6 1 1 3 2 5 3 1 3 2 1 6 6 6 5 (a) Construct an X-chart in conjunction with the R-chart, plot the first 3 sample observations. (5 + 5 = 10 marks) (b) The company has designed its packaging and delivery process to deliver orders to a customer within 3 business days +1 day, which it tells customers. Using the process mean and control limits developed in (a) compute the process capability index, and comment on the capability of the process to meet the company's delivery commitment. (hint: 30 =A,R and X = X ) (4 marks) (c) Suppose the company wants to tell customers it can deliver within 4 business days N days, given the company's current process capability, what should be the smallest value for N