Problem

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.

$$\bar{x} = 42.8 \qquad \sum (x - \bar{x})^2 = 941.5$$

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