A die is a specialized tool used in manufacturing industries

A die is a specialized tool used in manufacturing industries to cut or shape material mostly using a press. Products made with dies range from simple paper clips to complex pieces used in advanced technology.
An article reported that, in a study of a particular wafer inspection process, 356 dies were examined by an inspection probe and 245 of these passed inspection. What is the estimated proportion of wafers that passed inspection? (Round your answers to three decimal places.)  
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.)
95%CI

  ,

Solution

the estimated proportion = 245/356 = 0.688

Given a=0.05, Z(0.025) = 1.96 (from standard normal table)

SO the lower bound is

p - Z*sqrt(p*(1-p)/n) =0.688 - 1.96*sqrt(0.688*(1-0.688)/356) =0.640

So the upper bound is

p + Z*sqrt(p*(1-p)/n) =0.688 + 1.96*sqrt(0.688*(1-0.688)/356) =0.736