find the critical value zα/2 that corresponds to the confidence level 91%. zα/2 = (round to two decimal…

Explanation:

Step1: Calculate $\alpha$

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

Step2: Calculate $\alpha/2$

Divide $\alpha$ by 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 $\alpha/2 = 0.045$. Looking up the $z$ - value in the standard normal table (or using a calculator with a normal - distribution function), the area to the left of $z_{\alpha/2}$ is $1 - 0.045=0.955$. Using a standard normal table or a calculator (e.g., invNorm(0.955) on a TI - 84 Plus), we get $z_{\alpha/2}\approx1.69$.

Answer:

$1.69$