13. Defective Lightbulbs The table lists the number of defective 60-watt lightbulbs found in samples of 100 bulbs selected over 25 days from a manufacturing process. Assume that during this time the manufacturing process was not producing an excessively large fraction of defectives

a. Construct a p chart to monitor the manufacturing process, and plot the data.

b. How large must the fraction of defective items be in a sample selected from the manufacturing process before the process is assumed to be out of control?

c. During a given day, a sample of 100 items is selected from the manufacturing process and 15 defective bulbs are found. If a decision is made to shut down the manufacturing process in an attempt to locate the source of the implied controllable variation, explain how this decision might lead to erroneous conclusions.

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Day 1 2 3 4 5 6 7 8 9 10 Defectives 4 Day 2 5 8 3 4 4 5 6 1 11 12 13 14 15 16 17 18 19 20 Defectives 2 4 3 4 0 2 3 1 40 Day 21 22 23 24 25 Defectives 2 2 3 5 3