Calculate the standard score of the given X value, X=29.8
, where μ=25.1
 and σ=23.3
 and indicate on the curve where z will be located. Round the standard score to two decimal places.

The standard score (also known as the **z-score**) is calculated using the formula:

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

where:
- \(X\) is the value of interest (29.8 in this case),
- \(\mu\) is the mean (25.1), and
- \(\sigma\) is the standard deviation (23.3).

Substituting the values:

\[
z = \frac{29.8 - 25.1}{23.3} = \frac{4.7}{23.3} \approx 0.20
\]

So, the **standard score (z)** is approximately **0.20**.

This means the value \( X = 29.8 \) is 0.20 standard deviations above the mean.

### Z-location on the curve:
In a standard normal distribution curve, the z-score of 0.20 is slightly to the right of the mean (which is 0). It indicates that 29.8 is just above the average, but still close to the center of the distribution.

Would you like an image of the curve showing where this z-score would be located? Let me know if you'd like further details or if you have any questions!

Here are 5 related questions:
1. How does the z-score change if the standard deviation increases?
2. What does a negative z-score represent?
3. What is the probability of finding a z-score above 0.20?
4. How do you interpret a z-score of 1?
5. Can a z-score be greater than 3?

**Tip:** The z-score helps to compare different data points from different distributions by converting them into a standard form.

Calculate the standard score of the given X value, X=29.8, where μ=25.1 and σ=23.3 and indicate on the curve where z will be located. Round the standard score to two decimal places.

Learn how to calculate the standard score (z-score) for the value X=29.8, with a mean (μ) of 25.1 and standard deviation (σ) of 23.3. This problem illustrates key statistical concepts such as the normal distribution and how to determine where a z-score is located on the curve. Suitable for high school students in Grades 10-12.

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