7 Bob is a self-employed builder. In the past his weekly income had mean \(
) 546\( and standard deviation \)\\( 120\). Following a change in Bob's working pattern, his mean weekly income for 40 randomly chosen weeks was \(
) 581\(. You should assume that the standard deviation remains unchanged at \)\\( 120\).

1. Test at the \(2.5 \%\) significance level whether Bob's mean weekly income has increased.
   Bob finds his mean weekly income for another random sample of 40 weeks and carries out a similar test at the \(2.5 \%\) significance level.
2. Given that Bob's mean weekly income is now in fact \(
   ) 595$, find the probability of a Type II error.
   If you use the following lined page to complete the answer(s) to any question(s), the question number(s) must be clearly shown.