6 The continuous random variable \(R\) has the distribution \(\mathrm { N } \left( \mu , \sigma ^ { 2 } \right)\). The results of 100 observations of \(R\) are summarised by
$$\Sigma r = 3360.0 , \quad \Sigma r ^ { 2 } = 115782.84 .$$
- Calculate an unbiased estimate of \(\mu\) and an unbiased estimate of \(\sigma ^ { 2 }\).
- The mean of 9 observations of \(R\) is denoted by \(\bar { R }\). Calculate an estimate of \(\mathrm { P } ( \bar { R } > 32.0 )\).
- Explain whether you need to use the Central Limit Theorem in your answer to part (ii).