You schedule production of communications chips. After the chips are produced, they go to the QC department, where each chip must pass a 2-hour test. Over the past year, 5.0% of the chips have failed this test. You wish to choose a batch size that will yield as close as possible to 1,000 good chips, on average. What is the best batch size?

Question

Mathematics

Rhett Fitzpatrick

12 August, 21:58

You schedule production of communications chips. After the chips are produced, they go to the QC department, where each chip must pass a 2-hour test. Over the past year, 5.0% of the chips have failed this test. You wish to choose a batch size that will yield as close as possible to 1,000 good chips, on average. What is the best batch size?

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Aydan Buchanan · Answer 1

The best batch size is 1053.

Since 5% have failed, this means 95% have passed the test.

95% = 95/100 = 0.95

We can set up an equation to answer this:

0.95x = 1000

Divide both sides by 0.95:

0.95x/0.95 = 1000/0.95

x = 1052.6 ≈ 1053