Question

find the critical value ( z_{c} ) necessary to form a confidence interval at the level of confidence shown below.
( c = 0.82 )
( z_{c} = ) (round to two decimal places as needed.)

Explanation:

Step1: Calculate the significance level ($\alpha$)

The confidence level is $c = 0.82$. The significance level is $\alpha=1 - c$.
$$\alpha=1 - 0.82=0.18$$

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

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

Step3: Find the $z -$score

We want to find $z_c$ such that $P(Z>z_c)=0.09$, or equivalently $P(Z\leq z_c)=1 - 0.09 = 0.91$.
Looking up in the standard normal ($z -$) table (or using a calculator with a normal - distribution function, e.g., in Excel: =NORM.S.INV(0.91)), we get $z_c\approx1.34$

Answer:

$1.34$