To find the 30th percentile of the distribution, we need to determine the z-score corresponding to the 30th percentile and then use the z-score formula.

1. **Find the z-score** for the 30th percentile. The z-score for the 30th percentile is approximately **-0.524**.

2. **Apply the z-score formula**:
   \[
   X = \mu + z \times \sigma
   \]
   Where:
   - $\mu = 4200$ (mean)
   - $z = -0.524$ (z-score for the 30th percentile)
   - $\sigma = 250$ (standard deviation)

Let's calculate this.The 30th percentile of this distribution is approximately **$4,069.00**.

Would you like further details or have any questions?

Here are some related questions:

1. What is the 10th percentile of this distribution?
2. How would the 30th percentile change if the mean increased to $4,500?
3. What is the 50th percentile (median) of this distribution?
4. How do you find the 80th percentile of this distribution?
5. What percentage of bikes are priced between the 30th and 70th percentiles?

**Tip:** When finding percentiles, keep in mind that the 50th percentile corresponds to the median of the distribution.

Learn how to calculate the 30th percentile of a distribution using the z-score formula. This problem involves statistics and normal distribution concepts, including mean, standard deviation, and z-scores. Suitable for advanced high school students.

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