Question

Find zα/2 for the 94% confidence interval.

Answer 1

To determine \( z_{\alpha/2} \) for a 94% confidence interval, we first need to find \( \alpha \), which represents the total area in the tails of the normal distribution.

1. The confidence level is 94%, so:
\[
\alpha = 1 - 0.94 = 0.06
\]

2. Since the confidence interval is two-tailed, we split \( \alpha \) into two tails:
\[
\frac{\alpha}{2} = \frac{0.06}{2} = 0.03
\]

3. Next, we look for the \( z \)-score that corresponds to an area of \( 1 - 0.03 = 0.97 \) in the standard normal distribution.

You can use a standard normal distribution table or a calculator to find this value. The \( z \)-score that corresponds to an area of 0.97 is approximately:

\[
z_{0.03} \approx 1.881
\]

Thus, \( z_{\alpha/2} \) for a 94% confidence interval is approximately **1.881**.