6. A company produces a certain type of mug. The masses of these mugs are normally distributed with mean \(\mu\) and standard deviation 1.2 grams. A random sample of 5 mugs is taken and the mass, in grams, of each mug is measured. The results are given below.
\section*{\(\begin{array} { l l l l l } 229.1 & 229.6 & 230.9 & 231.2 & 231.7 \end{array}\)}
- Find a \(95 \%\) confidence interval for \(\mu\), giving your limits correct to 1 decimal place.
Sonia plans to take 20 random samples, each of 5 mugs. A 95\% confidence interval for \(\mu\) is to be determined for each sample.
- Find the probability that more than 3 of these intervals will not contain \(\mu\).