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 [22, 13, 15, 15]; Machine #2 measurements [ 14, 18, 12, 16]; Machine #3 measurements [ 22, 20, 14, 13]. Using the factors for three sigma control limits, what are x-bar chart upper and lower control limits?

a.

24.33and 8.007

b.

40.17and -7.833

c.

22.01and 10.33

d.

18.33and 14.01