Answer
$\color{blue}{\approx 29.85}$
Work Step by Step
Given $\mu=40, \sigma$ the unknown standard deviation. To find $\sigma$ given:
$\begin{align*}
P(20 \le Y\le 60) &= 0.50 \\
P\left(\frac{20-40}{\sigma}\le \frac{Y-\mu}{\sigma}\le \frac{60-40}{\sigma}\right) &= 0.50 \\
P\left(-\frac{20}{\sigma}\le Z\le\frac{20}{\sigma}\right) &= 0.50,\ Z\sim N(0,1) \\
2P\left( 0\le Z\le \frac{20}{\sigma} \right) &= 0.50 \qquad \text{[ since }\ f_z(z)\ \text{is symmetric about}\ z=0\ ] \\
P\left( 0\le Z\le \frac{20}{\sigma} \right) &= 0.25 \\
P(Z\lt 0) + P\left( 0\le Z\le \frac{20}{\sigma} \right) &= 0.5 + 0.25,\quad \text{[ since }\ P(Z\lt 0) = 0.5\ ] \\
P\left(Z\le \frac{20}{\sigma} \right) &= 0.75 \\
F_Z\left(\frac{20}{\sigma}\right) &\approx F_Z(0.67) \qquad \text{[ see Appendix Table A.1, pp. 675-6 ]} \\
\frac{20}{\sigma} &\approx 0.67, \text{[ since}\ 0\lt F_Z(z)\lt 1 \ \text{is one-to-one}\ ] \\
\sigma &\approx \frac{20}{0.6745} \\
\sigma\ &\color{blue}{\approx 29.85}
\end{align*}$
