What is the Z-value that corresponds to an \( 78 \% \) confidence interval? \( \begin{array}{llll}\text { A) }-2.1 & \text { B) } 1.23 & \text { C) } 1.20 & \text { D) }-1.61\end{array} \)

To find the Z-value corresponding to a \( 78\% \) confidence interval, you first calculate the area in the tails. Since the total area under the normal curve is \( 1 \), a \( 78\% \) confidence level leaves \( 22\% \) in the tails, or \( 11\%\) in each tail. This requires looking up the \( 89\% \) percentile (which is \( 1 - 0.11 = 0.89\)) in the Z-table. The Z-value that corresponds roughly to \( 0.89 \) is \( 1.23\). So, the answer is \( B) 1.23 \). For a \( 78\% \) confidence interval, utilizing the standard normal distribution is essential—making it more accessible than you might think! Most statistics textbooks or online resources will provide Z-tables or calculators for finding these values. If you're ever unsure, don’t hesitate to consult these references for improved clarity and confidence in your stats game!