Answer
$\color{blue}{1.349}$
Work Step by Step
$\underline{z_{.25}}$
$\begin{align*}
P(Z\ge z_{.25}) &= .25 \\
1-P(Z\ge z_{.25}) &= 1-.25 \\
P(Z \lt z_{.25}) &= 0.75 \\
P(Z\le z_{.25}) &= 0.75,\quad Z\sim N(0,1), \text{continuous pdf} \\
F_Z(z_{.25}) &= .75 \\
F_Z(z_{.25}) &\approx F_Z(0.6745) \qquad \text{[ see Appendix Table A.1, pp. 675-6; interpolate ]} \\
z_{.25} &\approx 0.6745 \qquad \text{[ since}\ F_Z(z)\ \text{is one-to-one for}\ 0 < F_Z(z) < 1\ ]
\end{align*}$
$\underline{z_{.75}}$
$\begin{align*}
P(Z\ge z_{.75}) &= .75 \\
1-P(Z\ge z_{.75}) &= 1-.75 \\
P(Z \lt z_{.75}) &= 0.25 \\
P(Z\le z_{.75}) &= 0.25,\quad Z\sim N(0,1), \text{continuous pdf} \\
F_Z(z_{.75}) &= .25 \\
F_Z(z_{.75}) &\approx F_Z(-0.6745) \qquad \text{[ see Appendix Table A.1, pp. 675-6; interpolate ]} \\
z_{.25} &\approx -0.6745\qquad \text{[ since}\ F_Z(z)\ \text{is one-to-one for}\ 0 < F_Z(z) < 1\ ]
\end{align*}$
$\underline{Q}$
$\begin{align*}
Q &= z_{.25} - z_{.75} \\
&\approx 0.6745 - (-0.6745) \\
Q &\approx \color{blue}{1.349}
\end{align*}$
