A cylindrical piece is used in an assembly in which the weight is to be controlled. The tolerances on diameter and height, on the basis of five observations, are 2 ±0.06 cm

and 6 ±0.06 cm, respectively. Assume that the dimensions are independent of each other and are each normally distributed with a capability ratio of 1. What are the natural tolerance limits on the volume of the cylinder? If specifications on volume are 18.5 ±0.6 cm3, what proportion of the cylinders will be nonconforming, assuming normality? What is the Cp index? If the target volume is 18.5, what is the Cpm index?
Test a hypothesis to determine if Cp is less than 0.6 using α =0.05.

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TABLE 9-11 Operator I's pH Values Sample Number Measurement 1 Measurement 2 Measurement 1 Operator 2's pH Values Measurement 2 11 12 13 14 15 1234567890D CRAS 6.28 6.24 6.25 6.26 6.12 6.18 6.06 6.11 6.64 6.58 6.61 6.69 6.85 6.92 6.78 6.84 6.92 6.83 6.85 6.91 6.43 6.52 6.38 6.45 6.36 6.44 6.35 6.42 6.50 6.56 6.46 6.51 6.75 6.68 6.69 6.75 6.68 6.60 6.65 6.72 6.34 6.39 6.28 6.36 6.54 6.62 6.48 6.56 6.82 6.73 6.76 6.83 6.48 6.40 6.49 6.44 6.53 6.59 6.47 6.53