Question

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

( z_{alpha/2}=)
(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 have $\alpha=1 - 0.83 = 0.17$.

Step2: Calculate $\frac{\alpha}{2}$

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

Step3: Find the $z -$ value

We want to find $z_{\alpha/2}$ such that $P(Z>z_{\alpha/2})=\frac{\alpha}{2}=0.085$ or $P(Z\leq z_{\alpha/2})=1 - 0.085 = 0.915$.
Looking up in the standard normal ($z -$) table (or using a calculator with a normal - distribution function, e.g., in Excel =NORM.S.INV(0.915)), we find that $z_{\alpha/2}\approx1.37$.

Answer:

$1.37$