- Some biologists were studying a large group of wading birds. A random sample of 36 were measured and the wing length, \(x \mathrm {~mm}\) of each wading bird was recorded. The results are summarised as follows
$$\sum x = 6046 \quad \sum x ^ { 2 } = 1016338$$
- Calculate unbiased estimates of the mean and the variance of the wing lengths of these birds.
Given that the standard deviation of the wing lengths of this particular type of bird is actually 5.1 mm ,
- find a \(99 \%\) confidence interval for the mean wing length of the birds from this group.