Respuesta :
the 95% confidence interval for the proportion of all dies that pass the probe is [0.513,0.616].
What is sample proportion?
Sampling is frequently used to estimate the percentage of population that possesses a particular attribute, such as the percentage of all faulty goods which come off an assembly line or the percentage among all buyers that enter a store and make a purchase before leaving. The population proportion is indicated p, while the sample proportion is written p. Thus, if 43% of individuals visiting a business make a purchase before departing, p = 0.43; if 78 people enter the store and make a transaction, p=78/200=0.39.
The sample proportion is a random variable because it differs from sample to sample in ways that are impossible to anticipate in advance. When seen as a random variable, it will be represented by the letter P.
How to solve?
An article reported that in a study of a particular wafer inspection process, 356 dies were examined by an inspection probe and 169 of these passed the probe.
So,p'=201/356=0.56460
The 95% confidence interval for the proportion of all dies that passed the probe will be,
p∈[p'±zα/2√p'(1−p')/n]
p∈[0.56460±1.96×√0.56460(1−0.56460)356]
p∈[0.513,0.616]
So the 95% confidence interval is [0.513,0.616].
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