\begin{tabular}{l}\( z_{\alpha / 2} \) for the \( 87 \% \) confidence interval \\ \( z_{\alpha / 2}=\square \) \\ \hline\end{tabular}

To find \( z_{\alpha / 2} \) for an \( 87\% \) confidence interval, you first need to determine \( \alpha \). Since the confidence level is \( 87\% \), \( \alpha = 1 - 0.87 = 0.13 \). Therefore, \( \alpha / 2 = 0.065 \). You can then look up \( z_{0.065} \) in the standard normal distribution table, which gives you approximately \( 1.81 \). Now you have \( z_{\alpha / 2} \approx 1.81 \). This means that about \( 87\% \) of the data lies within the interval defined by \( \mu \pm 1.81\sigma \)! To ensure accuracy, double-check the standard normal table or use a calculator for the precise value, as it gives you a better grasp on how far the estimate extends based on the confidence level!