A Quality Analyst wants to construct a control chart for determining whether three machines, all producing the same product, are under control with regard to a particular quality variable. Accordingly, he sampled four units of output from each machine, with the following results : Machine #1 measurements [12, 20, 20, 19]; Machine #2 measurements [ 19, 21, 18, 16]; Machine #3 measurements [ 14, 16, 21, 21]. Using the factors for three sigma control limits, what are x-bar chart upper and lower control limits?

a.

22.95and 13.22

b.

24.88and 11.28

c.

19.88and 16.28

d.

38.08and -1.917