Below are monthly rents paid by 30 students who live off campus.
 
700

700

700

900

670

540

660

1,000

710

590

690

625

530

710

620

630

820

885

570

590

730

660

680

470

700

770

790

810

690

685

find the z value for 730

To find the z-score for a rent of 730, we first need to calculate the mean and standard deviation of the dataset. The z-score formula is given by:

\[
z = \frac{X - \mu}{\sigma}
\]

Where:
- \( X \) is the value for which we want to find the z-score (730 in this case),
- \( \mu \) is the mean (average) of the data,
- \( \sigma \) is the standard deviation of the data.

Let's calculate the mean and standard deviation.

1. **Mean**:
\[
\mu = \frac{\sum X_i}{n}
\]
where \( \sum X_i \) is the sum of all the rent values and \( n \) is the number of data points (30).

2. **Standard Deviation**:
\[
\sigma = \sqrt{\frac{\sum (X_i - \mu)^2}{n}}
\]
where \( X_i \) are the individual rent values.

Let's calculate these values.The mean rent \(\mu\) is approximately \(694.17\), and the standard deviation \(\sigma\) is approximately \(111.68\).

Using the formula for the z-score:
\[
z = \frac{730 - 694.17}{111.68} \approx 0.32
\]

So, the z-score for a rent of 730 is approximately \(0.32\).

Would you like further details or have any questions?

Here are five related questions you could explore:
1. How would the z-score change for a rent of 600?
2. What percentage of students pay rents above 730, assuming a normal distribution?
3. What is the range of rents within one standard deviation from the mean?
4. How does a rent of 1000 compare in terms of z-score?
5. What would be the z-score for the lowest rent in the dataset?

**Tip**: Z-scores allow you to compare how far a value is from the mean in terms of standard deviations.

Below are monthly rents paid by 30 students who live off campus. Find the z value for 730.

Discover how to calculate the z-score for a rent of 730 from a dataset of 30 students' monthly rents. Learn key concepts such as mean, standard deviation, and the z-score formula. Suitable for high school students in Grades 10-12.

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