Question

find the critical value ( z_{alpha / 2} ) that corresponds to a 91% confidence level.

a. 1.645
b. 1.75
c. 1.34
d. 1.70

Explanation:

Step1: Calculate the value of $\alpha$

The confidence level is $C = 91\%=0.91$. Using the formula $\alpha=1 - C$, we get $\alpha=1 - 0.91 = 0.09$.

Step2: Calculate the value of $\frac{\alpha}{2}$

Divide $\alpha$ by 2. So, $\frac{\alpha}{2}=\frac{0.09}{2}=0.045$.

Step3: Calculate the value of $1-\frac{\alpha}{2}$

Using the formula $1-\frac{\alpha}{2}$, we substitute $\frac{\alpha}{2}=0.045$ and get $1 - 0.045=0.955$.

Step4: Look up the $z$-value in the standard normal table

Looking up the $z$-value corresponding to a cumulative probability of $0.955$ in the standard normal ($z$) - table. The $z$-value for which $P(Z\leq z)=0.955$ is approximately $z = 1.70$.

Answer:

D. 1.70