6 The heights, \(h\) centimetres, of a random sample of 100 fully grown animals of a certain species were measured. The results are summarised below.
$$n = 100 \quad \Sigma h = 7570 \quad \Sigma h ^ { 2 } = 588050$$
- Find unbiased estimates of the population mean and variance.
- Calculate a \(99 \%\) confidence interval for the mean height of animals of this species.
Four random samples were taken and a \(99 \%\) confidence interval for the population mean, \(\mu\), was found from each sample. - Find the probability that all four of these confidence intervals contain the true value of \(\mu\).