Question

A random sample of 100 articles taken from a batch of 2000 articles with S. D. 0.048 shows that the average diameter of

the articles is 0.354. Find 95% confidence interval for the average diameter of this batch of 2000 articles. (Given area

under the normal curve between and is 0.475)

Answer 1

$95\%CI=(\bar x-z_{0.025}\frac{\sigma}{\sqrt{n}}\sqrt{\frac{N-n}{N-1}},\bar x+z_{0.025}\frac{\sigma}{\sqrt{n}}\sqrt{\frac{N-n}{N-1}})=$

$=(0.354-1.96\frac{0.048}{\sqrt{100}}\sqrt{\frac{2000-100}{2000-1}},0.354+1.96\frac{0.048}{\sqrt{100}}\sqrt{\frac{2000-100}{2000-1}})=$

$=(0.3448, 0.3632).$