4 The random variable \(Y\) has the distribution \(\mathrm { N } \left( \mu , \sigma ^ { 2 } \right)\). The results of 40 independent observations of \(Y\) are summarised by
$$\Sigma y = 3296.0 , \quad \Sigma y ^ { 2 } = 286800.40$$
- Calculate unbiased estimates of \(\mu\) and \(\sigma ^ { 2 }\).
- Use your answers to part (i) to estimate the probability that a single random observation of \(Y\) will be less than 60.0.
- Explain whether it is necessary to know that \(Y\) is normally distributed in answering part (i) of this question.