The diagram shows the curves with equations \(y = x^{-\frac{1}{2}}\) and \(y = \frac{5}{2} - x^{-\frac{1}{2}}\). The curves intersect at the points \(A \left( \frac{1}{4}, 2 \right)\) and \(B \left( 4, \frac{1}{2} \right)\).

(a) Find the area of the region between the two curves.

(b) The normal to the curve \(y = x^{-\frac{1}{2}}\) at the point \((1, 1)\) intersects the y-axis at the point \((0, p)\).

Find the value of \(p\).