Answer:
Consider the following explanation
Standard deviation = .4
Mean = 128.5
Explanation:
a. given mean = 128.5 standard devaition s.d =0.4 n= sample size 6
UCL = mean +3 Q/ sqrt n = 128.5 + 3 * 0.4 /sqrt 6 = 128.9899
LCL = mean - 3 Q/ sqrt n = 128.5 - 3 * 0. 4/ sqrt 6 = 128.0101
A process is said to be out-of control, if any of sample points fall beyond the control limits (below the LCLor above the UCL)
b. Is the process in control for a sample providing the following data?
(128.8 +128.2 +129.11+ 28.7+ 128.4 +129.2 )/ 6 = 127.33
Since in the above sample, one point (129.2) is above the UCL and no point is below LCL (lessthan 127.3), the process is said to be out-of-control
x= 127.333
c. Is the process in control for a sample providing the following data?
(129.3 +128.7 +128.6 6 129.2 +129.5 + 129.0) / 6 =129.05
Since in the above sample, four points (129, 129.2, 129.3, 129.5) are above the UCL and nopoint is below LCL (less than 127.3), the process is said to be out-of-control
x= 129.05