https://file.aiquickdraw.com/mathbot/file/1726444617139cz2ho87q.jpg

The problem in the image is asking for the **z-score** of Jenny's commute distance relative to the mean commute distance for all students at her institute.

### Given Data:
- Jenny's commute distance: \( x = 25 \) kilometers
- Mean commute distance: \( \mu = 20 \) kilometers
- Standard deviation: \( \sigma = 7 \) kilometers

### Formula for z-score:
\[
z = \frac{x - \mu}{\sigma}
\]

### Substituting the given values:
\[
z = \frac{25 - 20}{7} = \frac{5}{7} \approx 0.71
\]

Thus, the **z-score is approximately 0.71** (rounded to two decimal places).

### Interpretation of the z-score:
Jenny's commute distance is **0.71 standard deviations above the mean** commute distance of all students.

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Would you like more details or have any questions?

Here are some related questions to further your understanding:

1. What does it mean if the z-score is negative?
2. How can we interpret z-scores in different contexts (e.g., test scores)?
3. What would the z-score be if Jenny's commute was below the mean?
4. How can the standard deviation affect the z-score?
5. Why is the z-score useful in comparing data points?

**Tip**: The z-score tells you how many standard deviations a data point is from the mean, providing a way to compare relative positions across different datasets or populations.

Jenny attends a fashion institute that has no on-campus housing. The distance she commutes between her home and the institute is 25 kilometers. The mean distance commuted to campus among all students at the fashion institute is 20 kilometers with a standard deviation of 7 kilometers. Find the z-score of Jenny's commute distance relative to the commute distances among all the students at the institute.

Learn how to calculate the z-score for Jenny's commute distance. With a commute of 25 kilometers, a mean commute distance of 20 kilometers, and a standard deviation of 7 kilometers, this problem demonstrates key statistical concepts. Suitable for high school students in Grades 10-12.

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