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 [16, 15, 20, 19]; Machine #2 measurements [ 24, 13, 20, 24]; Machine #3 measurements [ 17, 23, 12, 22]. Using the factors for three sigma control limits, what are x-bar chart upper and lower control limits?

a. 25.32and 12.18

b. 27.93and 9.57

c. 21.18and 16.32

d. 45.75and -8.25