Answer:
Please see explanation below for answers
Step-by-step explanation:
Parameters:
Mean (μ)= 92 & Standard deviation (σ)= 4
a. Upper specification limit USL = 100+10 = 110 units while
Lower specification limit LSL = 100-10 = 90 units
b. Process Capability Index, Cpk = min[USL−μ/3σ,μ−LSL/3σ]
Cpk = min[110-92/12,92-90/12]
Cpk = min[1.5,0.17]
Cpk = 0.17
c. From (b) above, since Cpk >0, The process is still within the product specification limit.
From the normal distribution
z = USL−μ/σ;μ−LSL/σ
z = 4.5;0.5
z= 4.5 for the upper specification and 0.5 for the lower specification
Using the normal distribution table at z= 4.5;
0.000340% are defective at the upper limit.
Using the normal distribution table at z= 0.5;
30.15% are defective at the lower limit.
Therefore total % defect = 30.15%+0.000340%=30.15%