1 A construction company notes the time, \(t\) days, that it takes to build each house of a certain design. The results for a random sample of 60 such houses are summarised as follows.
$$\Sigma t = 4820 \quad \Sigma t ^ { 2 } = 392050$$
- Calculate a 98\% confidence interval for the population mean time.
- Explain why it was necessary to use the Central Limit theorem in part (a).