- Components are manufactured such that their length in mm is normally distributed with mean \(\mu\) and variance \(\sigma ^ { 2 }\). Below is a 95\% confidence interval for \(\mu\) calculated from a random sample of components.
(11.52, 13.75)
Using the same random sample,
- find a \(90 \%\) confidence interval for \(\mu\).
Four 90\% confidence intervals are found from independent random samples.
- Calculate the probability that only 3 of these 4 intervals will contain \(\mu\).