Find the value of 

*z*/α2

. Use a graphing calculator and round the answer to at least three decimal places.

*z*/α2

 for the 

94%

 confidence interval

To find the critical value \( z_{\alpha/2} \) for a 94% confidence interval, we need to identify the value of \( z \) that corresponds to the middle 94% of the standard normal distribution.

1. For a 94% confidence level, the significance level \( \alpha \) is:
   \[
   \alpha = 1 - 0.94 = 0.06
   \]

2. Since \( z_{\alpha/2} \) is the critical value that captures the middle 94%, we divide \( \alpha \) by 2:
   \[
   \alpha/2 = 0.03
   \]

3. Now, we need to find the \( z \)-score for which the area to the left is \( 1 - 0.03 = 0.97 \).

Using a graphing calculator or standard normal distribution table, we find that the \( z \)-score corresponding to 0.97 is approximately:
   \[
   z_{\alpha/2} \approx 1.881
   \]

So, for a 94% confidence interval, the value of \( z_{\alpha/2} \) rounded to three decimal places is:
   \[
   z_{\alpha/2} \approx 1.881
   \]

Would you like further details on how to find this value using different methods?

---

1. What is the significance level in a confidence interval?
2. How is the critical value related to the confidence level?
3. How do you interpret a 94% confidence interval in practical terms?
4. How would you calculate \( z_{\alpha/2} \) for different confidence levels?
5. Why is it useful to round \( z \)-scores to three decimal places?

**Tip:** When solving problems involving confidence intervals, remember that the \( z \)-score provides a way to measure how far values fall from the mean in units of standard deviation.

Find the value of z/α2. Use a graphing calculator and round the answer to at least three decimal places. z/α2 for the 94% confidence interval.

Learn how to calculate the critical value z_{α/2} for a 94% confidence interval. This solution uses confidence interval theory and the z-score formula, ideal for high school students in Grades 11-12.

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