A Quality Analyst wants to construct a control chart for determining whether three different 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, 14, 16, 16]; Machine #2 measurements [ 21, 12, 13, 12]; Machine #3 measurements [ 17, 20, 19, 22]. Using the factors for three sigma control limits, what are x-bar chart upper and lower control limits?

a.

41.17and -6.833

b.

19.33and 15.01

c.

23.01and 11.33

d.

25.33and 9.007