 = \displaystyle \int _0^{32}\dfrac {x}{16} \dfrac {1}{ \sqrt{2 \pi}} \phi \left(-2+ \dfrtac {k}{16} \tight) \text {d}x+16= \displaystyle \int _0^{32}\dfrac {1}{16} \dfrac {x}{ \sqrt{2 \pi}}\text {exp} \left(- \dfrac{1}{2} t^2 \right) \text{d}t+16 \text { where }z=-2+ \dfrac {x}{16}