For \( C=95 \% \) then \( Z_{05}= \)

When the confidence level is \( C = 95\% \), it corresponds to a \( Z \)-score that can be found using a standard normal distribution table or calculator. Specifically, for \( \alpha = 1 - C = 0.05\), we split this into two tails, yielding \( \alpha/2 = 0.025\) in each tail. Therefore, \( Z_{0.05} \) for the upper critical value is approximately \( 1.96\). This means that about 95% of the distribution lies within \( \pm 1.96 \) standard deviations from the mean. To visualize this, you can think of a bell curve: about 95% of the area under the curve is found between \(-1.96 \) and \( 1.96\). This is an essential concept in statistics, particularly in constructing confidence intervals and hypothesis testing!