An article reported that, in a study of

Answered question

2022-04-27

An article reported that, in a study of a particular wafer inspection process, 356 dies were examined by an inspection probe and 239 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.)

Answer & Explanation

nick1337

nick1337

Expert2022-05-18Added 777 answers

n = 356

x = 239

p^ = x / n = 239 / 356 = 0.671

1 -p^ = 1 - 0.0.671 = 0.329

At 95% confidence level the z is ,

α = 1 - 95% = 1 - 0.95 = 0.05

α / 2 = 0.05 / 2 = 0.025

Zα/2 = Z0.025 = 1.960

Margin of error = E = Zα/2 ×p^×(1-p^)n 

= 1.960 ×0.671 × 0.329356 

= 0.049

95 % confidence interval for population proportion p is ,

p^- E < P < p^ + E

0.671 - 0.049 < p < 0.671 + 0.049


0.622 < p < 0.720

The 95% confidence interval for the population proportion p is : (0.622, 0.720)

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