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The question in the image asks to find the 60th percentile of the sample mean and round the answer to at least one decimal place.

To solve this:

1. **Percentile and the Normal Distribution**: The 60th percentile corresponds to a z-score of approximately **0.2533** in the standard normal distribution (you can find this from a z-table or calculator for the 0.60 cumulative probability).

2. **Using the Central Limit Theorem**: If the sample mean follows a normal distribution, we can use the formula for the z-score:
   \[
   z = \frac{X - \mu}{\sigma/\sqrt{n}}
   \]
   Where:
   - \( X \) is the sample mean corresponding to the 60th percentile,
   - \( \mu \) is the population mean,
   - \( \sigma \) is the population standard deviation,
   - \( n \) is the sample size.

3. **Solve for \( X \)** (the 60th percentile):
   \[
   X = \mu + z \times \frac{\sigma}{\sqrt{n}}
   \]
   You will need the values for the population mean \( \mu \), standard deviation \( \sigma \), and sample size \( n \) to compute this.

If you provide those values, I can help you find the 60th percentile of the sample mean!

Do you want to proceed with this? Feel free to provide any missing values, and I'll solve it for you.

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### Related Questions:
1. What is the z-score for other percentiles like the 50th or 90th percentile?
2. How does sample size \( n \) affect the width of the confidence interval for the sample mean?
3. Why does the Central Limit Theorem ensure that the sample mean follows a normal distribution?
4. What is the effect of standard deviation on the variability of the sample mean?
5. How do you interpret the result of a percentile in the context of income distribution?

**Tip**: When dealing with percentiles, using a z-score table can quickly help you determine the associated probability or value for a given distribution.

Find the 60th percentile of the sample mean. Round the answer to at least one decimal place.

Learn how to find the 60th percentile of the sample mean by using the z-score from the standard normal distribution and applying the Central Limit Theorem. This example demonstrates how to calculate the sample mean's percentile with step-by-step explanations, suitable for college-level statistics.

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