3 The masses, \(m \mathrm {~kg}\), of packets of flour are normally distributed. The mean mass is supposed to be 1.01 kg . A quality control officer measures the masses of a random sample of 100 packets. The results are summarised below.
$$n = 100 \quad \Sigma m = 98.2 \quad \Sigma m ^ { 2 } = 104.52$$
- Test at the \(5 \%\) significance level whether the population mean mass is less than 1.01 kg .
- Explain whether it was necessary to use the Central Limit theorem in your answer to part (i).