7. A machine produces bricks. The lengths, \(x \mathrm {~mm}\), of the bricks are distributed \(\mathrm { N } \left( \mu , 2 ^ { 2 } \right)\). At the start of each week a random sample of \(n\) bricks is taken to check the machine is working correctly.
A test is then carried out at the \(1 \%\) level of significance with $$\mathrm { H } _ { 0 } : \mu = 202 \text { and } \mathrm { H } _ { 1 } : \mu < 202$$

1. Find, in terms of \(n\), the critical region of the test. The probability of a type II error, when \(\mu = 200\), is less than 0.05
2. Find the minimum value of \(n\).