Question

find the critical value $z_{\alpha / 2}$ that corresponds to the confidence level $84 \\%$.

$z_{\alpha / 2}=\square$
(round to two decimal places as needed.)

Explanation:

Step1: Calculate the significance level $\alpha$

The confidence level is \(C = 0.84\). Using the formula \(\alpha=1 - C\), we get \(\alpha=1 - 0.84=0.16\).

Step2: Calculate \(\frac{\alpha}{2}\)

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

Step3: Find the \(z\) - value

We want to find \(z_{\alpha/2}\) such that \(P(Z>z_{\alpha/2}) = 0.08\), or equivalently \(P(Z\leq z_{\alpha/2})=1 - 0.08 = 0.92\).
Looking up in the standard normal distribution table (or using a calculator with a normal - distribution function, e.g., for a TI - 84: invNorm(0.92, 0, 1)), we find \(z_{\alpha/2}\approx1.41\).

Answer:

\(1.41\)