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To find the 20th percentile of the sample mean, you typically need the following information:

1. The sample mean.
2. The standard deviation (or standard error if referring to the distribution of sample means).
3. The sample size.
4. The z-score corresponding to the 20th percentile from the standard normal distribution.

### General Formula:
If we are working with a normally distributed sample mean, the formula for the \( p \)-th percentile of the sample mean distribution is:

\[
P_p = \mu + z_p \times \left( \frac{\sigma}{\sqrt{n}} \right)
\]

Where:
- \( \mu \) is the sample mean.
- \( \sigma \) is the population standard deviation (or standard deviation of the sample mean distribution).
- \( n \) is the sample size.
- \( z_p \) is the z-score corresponding to the desired percentile (for the 20th percentile, \( z_p \approx -0.8416 \)).

If you can provide the sample mean, standard deviation (or standard error), and sample size, I can help you complete this calculation.

Would you like to provide those details?

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Relative Questions:
1. What is the sample mean and standard deviation in your dataset?
2. How many observations are in your sample (sample size \( n \))?
3. Is the data approximately normally distributed, or do we need to use non-parametric methods?
4. Do you have access to a z-score table or need help finding the 20th percentile z-score?
5. Are there any assumptions about the population distribution that should be considered?

**Tip:** The 20th percentile z-score is negative, indicating it is below the mean. In practical terms, this means you're looking for a value less than the sample mean.

Find the 20th percentile of the sample mean. Round your answer to at least two decimal places.

This guide explains how to calculate the 20th percentile of the sample mean using statistical concepts such as percentiles, the normal distribution, and the standard error of the mean. Learn to apply the formula P_p = μ + z_p × (σ / sqrt(n)) and round your answer to two decimal places.

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