Question

find the critical value ( z_{alpha / 2} ) that corresponds to the confidence level 80%.
( z_{alpha / 2}=square )
(round to two decimal places as needed)

Explanation:

Step1: Calculate $\alpha$

The confidence level is $C = 80\%=0.8$. We know that $\alpha=1 - C$. So, $\alpha=1 - 0.8=0.2$.

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

$\frac{\alpha}{2}=\frac{0.2}{2}=0.1$.

Step3: Find the $z$-score

We want to find $z_{\alpha/2}$ such that $P(Z>z_{\alpha/2})=\frac{\alpha}{2}=0.1$. This is equivalent to finding $z$ such that $P(Z\leq z)=1 - 0.1 = 0.9$. Looking up in the standard normal distribution table (or using a calculator with a normal - distribution function, e.g., in Excel =NORM.S.INV(0.9)), we get $z_{\alpha/2}\approx1.28$.

Answer:

$1.28$