Question

find the critical value ( z_{alpha / 2} ) that corresponds to the confidence level ( 83% ).

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

Explanation:

Step1: Calculate $\alpha$

The confidence level is \(C = 83\%=0.83\). Using the formula \(\alpha=1 - C\), we get \(\alpha=1 - 0.83 = 0.17\).

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

Divide \(\alpha\) by 2. So, \(\frac{\alpha}{2}=\frac{0.17}{2}=0.085\).

Step3: Calculate \(1-\frac{\alpha}{2}\)

Using the formula \(1-\frac{\alpha}{2}\), we have \(1 - 0.085=0.915\).

Step4: Find \(z_{\alpha/2}\)

Look up the value \(0.915\) in the standard - normal (z - score) table. The \(z\) - score corresponding to a cumulative probability of \(0.915\) is \(z_{\alpha/2}\approx1.37\).

Answer:

\(1.37\)