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 [21, 20, 21, 12]; Machine #2 measurements [ 18, 23, 12, 20]; Machine #3 measurements [ 13, 15, 23, 15]. Using the factors for three sigma control limits, what are x-bar chart upper and lower control limits?

a.

20.45and 15.05

b.

27.95and 7.55

c.

47.75and -12.25

d.

25.05and 10.45