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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 186 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 between 0.470 and 0.574

Step-by-step explanation:

Confidence interval can be calculated as p±ME where

  • p is the sample proportion of dies that pass the probe
  • ME is the margin of error

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 corresponding statistic in 95% confidence level (1.96)
  • p is the sample proportion ([tex]\frac{186}{356}=0.522[/tex])
  • N is the sample size (356)

Using the numbers in the formula we get

ME=[tex]\frac{1.96*\sqrt{0.522*0.478}}{\sqrt{356} }[/tex] ≈0.052

then the 95% confidence interval would be 0.522±0.052

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