Question

in a study of a particular wafer inspection process 356 dies were examined by an inspection probe and 188 of these passed the probe. Assuming a stable process, calculate a 90% (two-sided) confidence interval for the proportion of all dies that pass the probe. (Round your answers to three decimal places.) ,

Answer 1

Solution :

Given that,

n = 356

x = 188

= x / n =188 / 356 = 0.528  

1 - = 1 - 0528. = 0.472

At 90% confidence level the z is ,

= 1 - 90% = 1 - 0.90 = 0.10

/ 2 = 0.10 / 2 = 0.05

Z_/2 = Z_0.05 = 1.645

Margin of error = E = Z _{/ 2} * (( * (1 - )) / n)

= 1.645 * (((0.528 * 0.472) / 356) = 0.044

A 90 % confidence interval for population proportion p is ,

- E < P < + E

0.528 - 0.044 < p < 0.528 + 0.044

0.484 < p < 0.527

The 90% confidence interval for the population proportion p is : ( 0.484 ,0527)