3 A random sample of 80 precision-engineered cylindrical components is checked as part of a quality control process. The diameters of the cylinders should be 25.00 cm . Accurate measurements of the diameters, \(x \mathrm {~cm}\), for the sample are summarised by $$\Sigma ( x - 25 ) = 0.44 , \quad \Sigma ( x - 25 ) ^ { 2 } = 0.2287 .$$

1. Calculate a \(99 \%\) confidence interval for the population mean diameter of the components.
2. For the calculation in part (i) to be valid, is it necessary to assume that component diameters are normally distributed? Justify your answer.