2 A random variable \(C\) has the distribution \(\mathrm { N } \left( \mu , \sigma ^ { 2 } \right)\). A random sample of 10 observations of \(C\) is obtained, and the results are summarised as
$$n = 10 , \Sigma c = 380 , \Sigma c ^ { 2 } = 14602 .$$
- Calculate unbiased estimates of \(\mu\) and \(\sigma ^ { 2 }\).
- Hence calculate an estimate of the probability that \(C > 40\).