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 [13, 18, 20, 12]; Machine #2 measurements [ 13, 23, 18, 16]; Machine #3 measurements [ 21, 23, 20, 18]. Using the factors for three sigma control limits, what are x-bar chart upper and lower control limits?

a.

23.51and 12.32

b.

25.74and 10.1

c.

40.92and -5.083

d.

19.99and 15.85