Question

find the critical value $z_{c}$ necessary to form a confidence interval at the level of confidence shown below. c = 0.83 $z_{c}=square$ (round to two decimal places as needed.)

Explanation:

Step1: Calculate the significance level $\alpha$

$\alpha = 1 - c=1 - 0.83 = 0.17$

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

$\frac{\alpha}{2}=\frac{0.17}{2}=0.085$

Step3: Find the $z -$ value

We want to find $z_c$ such that the area to the right of $z_c$ under the standard - normal curve is $\frac{\alpha}{2}=0.085$. Looking up in the standard - normal table (or using a calculator with a normal - distribution function), the $z$ - value corresponding to an area of $1 - 0.085 = 0.915$ is $z_c\approx1.37$.

Answer:

$1.37$