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Chicken Eggs A farmer focusing on the production of eco-friendly chicken eggs collects the following data about his output In
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Answer #1

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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