The length of industrial filters is a quality characteristic of interest. Thirty samples, each of size 5, are chosen fro

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The length of industrial filters is a quality characteristic ofinterest. Thirty samples, each of size 5, are chosen from theprocess. The data yield an average length of 110 mm, with theprocess standard deviation estimated to be 4 mm. a) Find the warning limits (2 σ ) for a control chart for theaverage length.b) Find the 3σ control limits. What is the probability of a type Ierror? c) If the process mean shifts to 112 mm, what are the chances ofdetecting this shift by the third sample drawn after theshift? d) What is the chance of detecting the shift for the first time onthe second sample point drawn after the shift?e) What is the ARL for a shift in the process mean to 112 mm (for3σ control limits)? How many samples, on average, would ittake to detect a change in the process mean to 116 mm?