Problem

The times taken by members of a large quiz club to complete a challenge have a normal distribution with mean $\mu$ minutes. The times, $x$ minutes, are recorded for a random sample of 8 members of the club. The results are summarised as follows, where $\bar{x}$ is the sample mean.

$\bar{x} = 33.8 \qquad \sum (x - \bar{x})^2 = 94.5$

Find a 95% confidence interval for $\mu$.