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 [15, 18, 17, 18]; Machine #2 measurements [ 14, 24, 19, 23]; Machine #3 measurements [ 21, 13, 23, 17]. Using the factors for three sigma control limits, what are x-bar chart upper and lower control limits?

a.

20.57and 16.43

b.

24.1and 12.9

c.

41.5and -4.5

d.

26.32and 10.68