The times taken by members of a large cycling club to complete a cross-country circuit have a normal distribution with mean \(\mu\) minutes. The times taken, \(x\) minutes, are recorded for a random sample of 14 members of the club. The results are summarised as follows, where \(\bar{x}\) is the sample mean.
\(\bar{x}=42.8 \quad \sum(x-\bar{x})^{2}=941.5\)

Find a \(95 \%\) confidence interval for \(\mu\).