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 [23, 12, 14, 12]; Machine #2 measurements [ 15, 17, 18, 16]; Machine #3 measurements [ 19, 14, 21, 13]. Using the factors for three sigma control limits, what are x-bar chart upper and lower control limits?

a.

38.17and -5.833

b.

18.15and 14.19

c.

23.65and 8.687

d.

21.52and 10.81