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The question is asking you to find the **critical z-value** for a right-tailed test with a significance level of \(\alpha = 0.07\), assuming the data follows a normal distribution.

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### Steps to Solve:

1. **Identify the cumulative probability**:
   - For a right-tailed test with \(\alpha = 0.07\), the cumulative probability \(P(Z < z)\) corresponds to \(1 - \alpha = 1 - 0.07 = 0.93\).

2. **Find the z-value**:
   - Using a standard normal distribution table or a z-score calculator, find the z-value corresponding to a cumulative probability of 0.93.

   From the z-score table or calculator:
   \[
   z \approx 1.48
   \]

3. **Round to two decimal places**:
   - The critical z-value is \(z = 1.48\).

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### Final Answer:
\[
z = 1.48
\]

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Would you like further details about how to use a z-table or other calculations? Let me know!

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### Related Questions:
1. What is the z-value for a two-tailed test with \(\alpha = 0.05\)?
2. How do you calculate a z-value using the cumulative distribution function (CDF)?
3. Why is the significance level \(\alpha\) important in hypothesis testing?
4. What are the differences between a left-tailed and right-tailed test?
5. How do critical values relate to p-values in hypothesis testing?

### Tip:
For precise critical values, using statistical software or a z-table can save time and ensure accuracy!

Find the critical z values. Assume that the normal distribution applies. Right-tailed test; α = 0.07.

Learn how to find the critical z-value for a right-tailed test with a significance level of α = 0.07. This solution explains the steps to calculate the cumulative probability and use the standard normal distribution to find the z-value, suitable for students in advanced statistics courses.

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