Given:
[tex]Z=\frac{X-\mu}{\sigma}[/tex]a) Where,
[tex]\begin{gathered} X_1=33,X_2=66 \\ \sigma=12,\mu=43 \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} Z_1=\frac{33-43}{12}=-\frac{10}{12}=-0.83333\approx-0.8333 \\ Z_2=\frac{66-43}{12}=1.91666\approx1.9167 \end{gathered}[/tex]Hence, the probability will be
[tex]P(Z_1Therefore, the answer is 0.22998 or 22.998%.b) Where
[tex]X=39,\mu=43,\sigma=12[/tex]Therefore,
[tex]Z=\frac{39-43}{12}=-0.33333[/tex]Then
[tex]P(X>Z)=0.63056[/tex]Hence, the answer is 0.63056 or 63.056%.