Question

find ( z_{alpha/2} ) for the ( 84% ) confidence interval (draw the graph and show all your work)

Explanation:

Step1: Calculate the value of \(\alpha\)

The confidence level \(C = 0.84\). We know that \(\alpha=1 - C\). So, \(\alpha=1 - 0.84=0.16\).

Step2: Calculate the value of \(\frac{\alpha}{2}\)

\(\frac{\alpha}{2}=\frac{0.16}{2}=0.08\).

Step3: Find the \(z\) - value

We want to find \(z_{\alpha/2}\) such that \(P(Z>z_{\alpha/2})=\frac{\alpha}{2} = 0.08\), or \(P(Z\leq z_{\alpha/2})=1 - 0.08=0.92\).
Looking up in the standard normal table (or using a calculator with a normal - distribution function, e.g., \(z=\text{NORM.S.INV}(0.92)\) in Excel), we find that \(z_{\alpha/2}\approx1.41\).

Answer:

\(z_{\alpha/2}\approx1.41\)