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, 19, 24, 21]; Machine #2 measurements [ 20, 18, 18, 17]; Machine #3 measurements [ 15, 22, 22, 19]. Using the factors for three sigma control limits, what are x-bar chart upper and lower control limits?

a.

40.92and -3.083

b.

24.27and 13.56

c.

20.9and 16.94

d.

26.4and 11.44