Question

find the critical value $z_{alpha/2}$ that corresponds to the given confidence level. 91% $z_{alpha/2}=square$ (round to two decimal places as needed.)

Explanation:

Step1: Calculate $\alpha$

The confidence level is $C = 91\%=0.91$. We know that $\alpha=1 - C$. So, $\alpha = 1- 0.91=0.09$.

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

$\frac{\alpha}{2}=\frac{0.09}{2}=0.045$.

Step3: Find the $z$-value

We want to find $z_{\alpha/2}$ such that the area to the right of $z_{\alpha/2}$ under the standard - normal curve is $\frac{\alpha}{2}=0.045$. Looking up in the standard - normal table (or using a calculator with a normal - distribution function), the area to the left of $z_{\alpha/2}$ is $1 - 0.045 = 0.955$. The $z$-value corresponding to an area of $0.955$ is approximately $1.69$.

Answer:

$1.69$