The manager of a building-supplies company randomly samples incoming lumber to see whether it meets quality specifications. From each shipment, 100 pieces of 2 × 4 lumber are inspected and judged according to whether they are first (acceptable) or second (defective) grade. The proportions of second-grade 2 × 4s recorded for 30 shipments were as follows:

Construct a control chart for the proportion of second-grade 2 × 4s in samples of 100 pieces of lumber. Explain how the control chart can be of use to the manager of the building-supplies company.

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