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Find each of the following. Enter your answers rounded to at least two decimal places. Part 1 of 5 \( z_{\alpha / 2} \) for the \( 95 \% \) confidence interval

Ask by Mejia Higgins. in the United States
Mar 11,2025

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\( z_{\alpha / 2} \approx 1.96 \)

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For a \( 95\% \) confidence interval, \( z_{\alpha / 2} \) corresponds to the critical value that captures the middle \( 95\% \) of the standard normal distribution. This means that \( \alpha = 1 - 0.95 = 0.05 \), and thus \( \alpha/2 = 0.025 \). The critical value \( z_{\alpha / 2} \) is found at the \( 97.5\% \) percentile of the standard normal distribution. Therefore, \( z_{0.025} \approx 1.96 \). So, for a \( 95\% \) confidence interval, \( z_{\alpha / 2} \approx 1.96 \).

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