1. Use the relation between $E$ and $B$ in free space

For a plane electromagnetic wave in free space,

$E = cB$

where $c = 3 \times 10^8\ \text{m s}^{-1}$.

So,

$B = \frac{E}{c}$

2. Substitute the given electric field

Given,

$E_y = 9.3\ \text{V m}^{-1}$

Hence,

$B_z = \frac{9.3}{3 \times 10^8}$

$B_z = 3.1 \times 10^{-8}\ \text{T}$

3. Determine the direction

The wave travels along the $+x$ direction. For an electromagnetic wave,

$\vec{E} \times \vec{B} \text{ is along the direction of propagation}$

Given $\vec{E}$ is along $+y$, we need $\vec{B}$ such that

$\hat{j} \times \hat{k} = \hat{i}$

which is along $+x$.

So the magnetic field is along $+z$.

Thus,

$\boxed{B_z = 3.1 \times 10^{-8}\ \text{T}}$

4. Compare with options

This matches Option C.

5. Compare with stored correct answer

Stored correct answer: C

Our derived answer: C

So, the answer agrees with the stored correct answer.