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?

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

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KarpaT KarpaT · Answer 2 · 2022-07-28T08:12:36+02:00

The best batch size has approximately 1053 chips.

What is a word problem?

A word problem is a verbal description of a problem situation. It consists of few sentences describing a 'real-life' scenario where a problem needs to be solved by way of a mathematical calculation.

For the given situation,

Percentage of chips failed the test = 5.0%

Then, percentage of good chips = 100-5

⇒ 95% = 0.95

Number of possible good chips = 1000

This equation for best batch size could be

[tex]0.95x = 1000[/tex]

⇒ [tex]x=\frac{1000}{0.95}[/tex]

⇒ x = 1052.63 ≈ 1053

Hence we can conclude that the best batch size has approximately 1053 chips.

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