In Chapter 12 we use a shortcut rule of adjust it towards the mean to save you having the consider the p-value.
So if we were calculating the p-value with our value of 45 we go towards the nearest critical region (which is the -1.96 one as our value is smaller than the mean) and so the p-value will be \(P(X \leq 45)\) using your chapter 8 knowledge this is equivalent to \(P(X \leq 45.5)\).
Similarly if we have a value of, say 55, the p-value will go towards the nearest critical region (which is 1.96 as our value is bigger than the mean) and so the p-value will be \(P(X \geq 45)\) using your chapter 8 knowledge this is equivalent to \(P(X \geq 44.5)\).
So you see - the towards the mean is a handy shortcut when calculating continuity corrections for hypothesis tests.