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 [24, 19, 17, 24]; Machine #2 measurements [ 14, 16, 15, 21]; Machine #3 measurements [ 17, 17, 17, 13]. Using the factors for three sigma control limits, what are x-bar chart upper and lower control limits?

a.

22.21and 13.45

b.

19.45and 16.21

c.

23.95and 11.71

d.

35.83and -0.1667