UCL = 50
LCL = 44
Mean = 47
standard deviation (s) = 2
As mean is centered, Cp will be used for capability score
Cp = (UCL - LCL)/(6*s) = (50-44)/(6*2) = 0.5
z value (<T1) = (T1-Mean)/s
z value for less than LCL of 44 is = (44 - 47)/2 = -1.5
Probability of values less than 44 is 0.0668 (Using z table)
z value for less than UCL of 50 is = (50 - 47)/2 = 1.5
Probability of values less than 50 is 0.9332 (Using z table)
So, probability of values within specification is = 0.9332 - 0.0668 = 0.8664 or 86.64%
For Cp = 2/3 = (UCL-LCL)/(6*s)
2/3 = (50-44)/(6*s)
s = 1.5
So, standard deviation needs to be reduced from 2 to 1.5
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