Find the critical value $z_{\alpha / 2}$ that corresponds to the confidence level $84 \%$.

Step 1 ：The critical value $z_{\alpha / 2}$ is a value on the standard normal distribution for which the area under the curve to the right of that value equals $\alpha / 2$.

Step 2 ：The confidence level is $1 - \alpha$, so in this case, $\alpha = 1 - 0.84 = 0.16$.

Step 3 ：Therefore, we need to find the value $z_{\alpha / 2}$ such that the area to the right of it is $0.16 / 2 = 0.08$.

Step 4 ：By looking up this value in a standard normal distribution table, or using a calculator or software that can do this, we find that $z_{\alpha / 2} \approx 1.41$.

Step 5 ：Final Answer: The critical value $z_{\alpha / 2}$ that corresponds to the confidence level $84 \%$ is approximately \(\boxed{1.41}\).