3. The lengths, \(X \mathrm {~mm}\), of the wings of adult blackbirds follow a normal distribution. A random sample of 5 adult blackbirds is taken and the lengths of the wings are measured. The results are summarised below
$$\sum x = 655 \text { and } \sum x ^ { 2 } = 85845$$
- Test, at the \(10 \%\) level of significance, whether or not the mean length of an adult blackbird's wing is less than 135 mm . State your hypotheses clearly.
- Find the \(90 \%\) confidence interval for the variance of the lengths of adult blackbirds' wings. Show your working clearly.