4 Part of an ecological study involved measuring the heights of trees in a young forest. In order to obtain an estimate of the mean height of all the trees in the forest, a random sample of 70 trees was selected and their heights measured. These heights, \(x\) metres, are summarised by \(\Sigma x = 246.6\) and \(\Sigma x ^ { 2 } = 1183.65\). The mean height of all trees in the forest is denoted by \(\mu\) metres.

1. Calculate a symmetric \(90 \%\) confidence interval for \(\mu\).
2. A student was asked to interpret the interval and said,
   "If 100 independent \(90 \%\) confidence intervals were calculated then 90 of them would contain \(\mu\)." Explain briefly what is wrong with this statement.
3. Four independent \(90 \%\) confidence intervals for \(\mu\) are obtained. Calculate the probability that at least three of the intervals contain \(\mu\).