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 [17, 23, 23, 17]; Machine #2 measurements [ 13, 13, 12, 21]; Machine #3 measurements [ 18, 16, 18, 16]. Using the factors for three sigma control limits, what are x-bar chart upper and lower control limits?

a. 34.25and 0.25

b. 21.39and 13.11

c. 18.78and 15.72

d. 23.03and 11.47