A quality analyst wants to construct a sample mean chart for controlling a packaging process. He knows from past experience that the process standard deviation is two ounces. Each day last week, he randomly selected four packages and weighed each. The data from that activity appear below.

	Weight
Day	Package 1	Package 2	Package 3	Package 4
Monday	23	22	23	24
Tuesday	23	21	19	21
Wednesday	20	19	20	21
Thursday	18	19	20	19
Friday	18	20	22	20

(a) Calculate all sample means and the mean of all sample means.

(b) Calculate upper and lower 2-sigma x-bar chart control limits that allow for natural variations.

(c) Based on the x-bar chart, is this process in control?

Question 2

1. Cartons of Plaster of Paris are supposed to weigh exactly 32 oz. Inspectors want to develop process control charts. They take ten samples of six boxes each and weigh them. Based on the following data, compute the lower and upper control limits and determine whether the process is in control.

   Sample	Mean	Range
   1	33.8	1.1
   2	34.6	0.3
   3	34.7	0.4
   4	34.1	0.7
   5	34.2	0.3
   6	34.3	0.4
   7	33.9	0.5
   8	34.1	0.8
   9	34.2	0.4
   10	34.4	0.3

Question 3

1. XYZ Ltd produces a product for which the annual demand is 10,000 units. Production averages 100 units per day, while demand is 40 units per day. Holding costs are $2.00 per unit per year, and setup cost is $200.00. (a) If the firm wishes to produce this product in economic batches, what size batch should be used?