Find the critical value z Subscript alpha divided by 2zα/2 that corresponds to the given confidence level.
91​%
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Part 1
z Subscript alpha divided by 2zα/2equals=enter your response here ​(Round to two decimal places as​ needed.)

To find the critical value \( z_{\frac{\alpha}{2}} \) for a confidence level of 91%, we can follow these steps:

1. The confidence level is given as 91%, which means the remaining area under the normal distribution (the significance level \( \alpha \)) is:
   \[
   \alpha = 1 - 0.91 = 0.09
   \]
   
2. Since we are looking for the critical value \( z_{\frac{\alpha}{2}} \), we need to divide \( \alpha \) by 2:
   \[
   \frac{\alpha}{2} = \frac{0.09}{2} = 0.045
   \]
   
3. Now, we need to find the \( z \)-score that corresponds to the cumulative probability of \( 1 - 0.045 = 0.955 \) (since we are looking for the value on the right side of the standard normal distribution).

4. Using a standard normal distribution table or a calculator, the \( z \)-score that corresponds to a cumulative probability of 0.955 is approximately:
   \[
   z_{\frac{\alpha}{2}} \approx 1.70
   \]

Therefore, the critical value \( z_{\frac{\alpha}{2}} \) for a 91% confidence level is approximately **1.70**.

Would you like more details or have any other questions?

Here are 5 related questions to expand on this:
1. How is the critical value used in hypothesis testing?
2. What is the significance level \( \alpha \), and how does it relate to confidence levels?
3. How do you calculate confidence intervals using the critical value?
4. What is the difference between a one-tailed and a two-tailed test in hypothesis testing?
5. Can you explain the relationship between the z-score and the area under the normal distribution curve?

**Tip:** Always double-check your confidence level and significance level to ensure you are using the right side of the normal distribution.

Find the critical value zα/2 that corresponds to the given confidence level of 91%. Round to two decimal places as needed.

This page explains how to find the critical value zα/2 for a 91% confidence level, using key statistical concepts such as confidence intervals and the standard normal distribution. The step-by-step guide helps you calculate the z-score for α/2, with a rounded value of approximately 1.70. Ideal for college or advanced high school students.

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