Find the critical value 

z Subscript alpha divided by 2zα/2 

that corresponds to the confidence level 

8080​%.

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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 \( z_{\alpha/2} \) corresponding to a confidence level of 80%, we follow these steps:

1. **Determine \(\alpha\)**:
   \[
   \alpha = 1 - \text{confidence level} = 1 - 0.80 = 0.20
   \]

2. **Calculate \(\alpha/2\)**:
   \[
   \frac{\alpha}{2} = \frac{0.20}{2} = 0.10
   \]

3. **Find the critical value**:
   We need to find \( z_{0.10} \). This value corresponds to the point where 10% of the distribution lies to the right. You can find this using a standard normal distribution table or calculator.

The critical value \( z_{0.10} \) is approximately **1.28**.

Thus, the critical value \( z_{\alpha/2} \) is:
\[
z_{\alpha/2} \approx 1.28
\]

**Final Answer**: \( z_{\alpha/2} \approx 1.28 \) (rounded to two decimal places).

Would you like further details on how to use this critical value, or do you have any other questions? Here are some related questions you might find interesting:

1. How does the confidence level affect the critical value?
2. What are the implications of using a lower confidence level?
3. How can we calculate critical values for other confidence levels?
4. What is the role of critical values in hypothesis testing?
5. Can you explain how to interpret a confidence interval using this critical value?

**Tip**: Always refer to a z-table or statistical software for more precise calculations of critical values.

Find the critical value zα/2 that corresponds to the confidence level 80%.

Explore how to find the critical value zα/2 for an 80% confidence level. This guide covers the calculation of α, the determination of α/2, and provides a step-by-step solution to find the critical value of approximately 1.28.

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