Solve the above questions step by step with complete calculations. Show all calculations.

Q.1(a) Nestle Drinks Inc., a producer of decaffeinated coffee, bottles Nescafe:. Each bottle should have a Net weight of 4oz. The machine that fills the bottles with coffee is new, and the Operations Manager wants to make sure that it is properly adjusted. He takes a sample of n=8 bottles and records the average and range in ounce for each of the sample. The data for 8 such samples is given below. Note that every sample consists of 8 bottles each. [4 Marks] [Time-15-Minutes] Required: a) Using this data, set up the control limits for the appropriate Control Chart(s). Do not draw the charts. b) Determine, whether the machine is properly adjusted and in statistical control? Q.1(b) M/s Nirala Sweets is selling its food products in the packing having net weight of 450 grams ( +20gm,10gms ). After having received complaints of short filling, a sample of 1000 such packets showed a standard deviation( ) of 15gm., which was not acceptable to customers. The consumers society asked the company to remain with in 5gm. of net quantity otherwise they will impose a penalty by stopping the consumers to buy the company's product. [3 Marks] [Time-15-Minutes] Required: i. What is the existing Process capability ratio (Cp) of M/s Nirala Sweets? ii. What max. " " should be maintained to just satisfy the customer? ii. What max. " " must be maintained to achieve 4-sigma capability