Question

find the critical value ( z_{alpha/2} ) that corresponds to the given confidence level.
82%
( z_{alpha/2}=) (round to two decimal places as needed.)

Explanation:

Step1: Calculate the significance level

The confidence level is \(C = 0.82\). The significance level \(\alpha=1 - C\).

$$ \alpha=1 - 0.82=0.18 $$

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

$$ \frac{\alpha}{2}=\frac{0.18}{2}=0.09 $$

Step3: Find the \(z\) - value

We want to find \(z_{\alpha/2}\) such that \(P(Z>z_{\alpha/2}) = 0.09\), or \(P(Z\leq z_{\alpha/2})=1 - 0.09 = 0.91\).
Using a standard normal table (or a calculator with a normal - distribution function, such as the inverse of the cumulative distribution function for the standard normal distribution \(\text{NORMSINV}\) in Excel), we find that \(z_{\alpha/2}\approx1.34\)

Answer:

\(1.34\)