6 Population \(A\) has a normal distribution with unknown mean \(\mu _ { A }\) and a variance of 18.8.
Population \(B\) has a normal distribution with unknown mean \(\mu _ { B }\) but with the same variance as Population \(A\). The random variables \(\bar { X } _ { A }\) and \(\bar { X } _ { B }\) denote the means of independent samples, each of size \(n\), from populations \(A\) and \(B\) respectively.

1. Find an expression, in terms of \(n\), for \(\operatorname { Var } \left( \bar { X } _ { A } - \bar { X } _ { B } \right)\).
2. Given that the width of a \(99 \%\) confidence interval for \(\mu _ { A } - \mu _ { B }\) is to be at most 5 , calculate the minimum value for \(n\).
   [0pt] [5 marks]