\( z_{\alpha / 2} \) for the \( 99 \% \) confidence interval \( z_{\alpha / 2}=\square \) Part 5 of 5

To find \( z_{\alpha/2} \) for a \( 99\% \) confidence interval, you first need to understand that \( \alpha \) represents the significance level. For a \( 99\% \) confidence interval, \( \alpha = 1 - 0.99 = 0.01 \). Since you need \( z_{\alpha/2} \), calculate \( \alpha/2 = 0.005 \). Looking up the \( 0.005 \) significance level in the standard normal distribution table, you find that \( z_{\alpha/2} \) corresponds to approximately \( 2.576 \). So, \( z_{\alpha/2} = 2.576 \). Integrating this concept into practical scenarios can illuminate its real-world significance! For example, businesses use confidence intervals to make informed decisions about sales forecasts, product quality checks, and understanding customer satisfaction. A \( 99\% \) confidence interval suggests that the results from a sample are highly reliable, which can influence inventory management or marketing strategies without excessive risk.