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 5 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 a = 0.05.

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