Answers
(a) Xbar and R chart are constructed as under:
Calculate sample Average (Xbar) and Range (R = difference of MAX and MIN value) for each day.
Calculate the Average of Xbars and R vaues of 40 days to get Xbarbar and Rbar
(b) Process standard deviation, 
= Rbar/d2 , where d2 is control chart constant = 2.326
= 1.12/2.326 = 0.4817
Cp = (USL-LSL)/6 = (3-0)/(6*0.4817) = 1.038
Cpu = (USL - 
)/3 = (3 - 1.6)/(3*0.4817) = 0.9688
Cpl = ( - LSL)/3 = (1.6 - 0)/(3*0.4817) = 1.1072
Cpk = MIN(Cpu, Cpl) = MIN(0.9608, 1.1072) = 0.9688
Cp and Cpk are less than 1.33. Therefore, the process is not capable of meeting specifications on 3 sigma quality.
c) z = (3-1.6)/0.4817 = 2.9064
P(z) = NORMSDIST(2.9064) = 0.9982
Percentage of ER visits expected to exceed the tolerance limit = 1 - 0.9982 = 0.0018 or 0.18 %
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