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An article reported that, in a study of a particular wafer inspection process, 356 dies were examined by an inspection probe and 210 of these passed the probe. Assuming a stable process, calculate a 95% (two-sided) confidence interval for the proportion of all dies that pass the probe. (Round your answers to three decimal places.

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Answer:

95% (two-sided) confidence interval for the proportion of all dies that pass the probe is 0.590±0.051 (between 0.539 and 0.641)

Step-by-step explanation:

Confidence Interval can be calculated using p±ME where

  • p is the samle proportion of dies that pass the probe ([tex]\frac{210}{356}[/tex] =0.590)
  • ME is the margin of error from the mean

and margin of error (ME) around the mean can be found using the formula

ME=[tex]\frac{z*\sqrt{p*(1-p)}}{\sqrt{N} }[/tex] where

  • z is the statistic in 95% confidence level (1.96)
  • p is the sample proportion ([tex]\frac{210}{356}=0.590[/tex]
  • N is the sample size (356)

Then ME=[tex]\frac{1.96*\sqrt{0.59*0.41}}{\sqrt{356} }[/tex]=0.051

95% confidence interval is 0.590±0.051

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