A manufacturer produces circular discs with diameter \(D \mathrm {~mm}\), such that \(D \sim \mathrm {~N} \left( \mu , \sigma ^ { 2 } \right)\). A random sample of discs is taken and, using tables of the normal distribution, a \(90 \%\) confidence interval for \(\mu\) is found to be
(118.8, 121.2)
Find a 98\% confidence interval for \(\mu\).
Hence write down a 98\% confidence interval for the circumference of the discs.
Using three different random samples, three \(98 \%\) confidence intervals for \(\mu\) are to be found.
Calculate the probability that all the intervals will contain \(\mu\).