3 The times, in minutes, taken by competitors to complete a puzzle have mean \(\mu\) and standard deviation 3 . The times taken by a random sample of 10 competitors are noted and the results are given below.
\(\begin{array} { l l l } 25.2 & 26.8 & 18.5 \end{array}\)
25.5
30.1
\(28.9 \quad 27.0\)
\(26.1 \quad 26.0\)
24.9

1. Stating a necessary assumption, calculate a \(97 \%\) confidence interval for \(\mu\).
2. Two more random samples, each of 10 competitors, are taken. Their times are used to calculate two more \(97 \%\) confidence intervals for \(\mu\). Find the probability that neither of these intervals contains the true value of \(\mu\).