Answer
(a) $\color{blue}{0.4808}$
(b) $\color{blue}{0.1951}$
(c) $\color{blue}{0.8554}$
(d) $\color{blue}{0.0099}$
(e) $\color{blue}{0.0000}$
Work Step by Step
(a)
$\begin{align*}
P(0\le Z\le 2.07) &= P(Z\le 2.07) - P(Z\lt 0) \\
&= P(Z\le 2.07) - P(Z\le 0) ,\quad Z\sim N(0,1), \text{continuous pdf} \\
&= F_Z(2.07) - F_Z(0) \\
&= 0.9808 - 0.5000 \qquad \text{[ see Appendix Table A.1, pp. 675-6 ]} \\
P(0\le Z\le 2.07) &= \color{blue}{0.4808}
\end{align*}$
(b)
$\begin{align*}
P(-0.64 \le Z \lt -0.11) &= P(Z\lt -0.11) - P(Z\lt -0.64) \\
&= P(Z\le -0.11) - P(Z\le -0.64),\quad Z\sim N(0,1), \text{continuous pdf} \\
&= F_Z(-0.11) - F_Z(-0.64) \\
&= 0.4562 - 0.2611 \qquad \text{[ see Appendix Table A.1, pp. 675-6 ]} \\
P(-0.64\le Z\lt -0.11) &= \color{blue}{0.1951}
\end{align*}$
(c)
$\begin{align*}
P(Z \gt -1.06) &= 1 - P(Z\le -1.06),\quad Z\sim N(0,1), \text{continuous pdf} \\
&= 1 - F_Z(-1.06) \\
&= 1 - 0.1446 \qquad \text{[ see Appendix Table A.1, pp. 675-6 ]} \\
P(Z\gt -1.06) &= \color{blue}{0.8554}
\end{align*}$
(d)
$\begin{align*}
P(Z \lt -2.33) &= P(Z\le -2.33),\quad Z\sim N(0,1), \text{continuous pdf} \\
&= F_Z(-2.33) \\
&= 0.0099 \qquad \text{[ see Appendix Table A.1, pp. 675-6 ]} \\
P(Z\lt -2.33) &= \color{blue}{0.0099}
\end{align*}$
(e)
$\begin{align*}
P(Z \ge 4.61) &= P(Z\gt 4.61),\quad Z\sim N(0,1) , \text{continuous pdf} \\
&= 1 - F_Z(4.61) \\
&= 1 - 1.0000 \qquad \text{[ see Appendix Table A.1, pp. 675-6 ]} \\
P(Z\ge 4.61) &= \color{blue}{0.0000}
\end{align*}$
