https://file.aiquickdraw.com/mathbot/file/17270669424289301aiod.jpg

In the image you uploaded, the distribution of \( X \) is given as:

\[
X \sim N(-67.5, 22.4)
\]

This notation describes a **Normal Distribution** with a mean \( \mu = -67.5 \) and a standard deviation \( \sigma = 22.4 \).

The image shows that the first part is asking for the kind of distribution, and the correct selection of **Normal Distribution** has already been made. In the second part, the mean \( \mu \) has been correctly filled in as \( -67.5 \).

Now, for the standard deviation \( \sigma \), the correct value from the distribution is **22.4**, which you can enter into the provided field.

Would you like further explanation about the normal distribution, or any additional details on the solution?

Here are 5 relative questions to deepen your understanding:
1. How is the normal distribution different from the standard normal distribution?
2. What role do the mean and standard deviation play in the shape of a normal distribution curve?
3. How would you calculate probabilities from this normal distribution using a z-score?
4. What is the empirical rule (68-95-99.7 rule) for normal distributions, and how does it apply here?
5. How can you use this distribution to make real-world predictions?

**Tip**: When you encounter a normal distribution, the mean represents the center of the data, and the standard deviation gives you a sense of the spread.

Let X ~ N(-67.5, 22.4). What kind of distribution is X? What is the mean and standard deviation of the distribution?

Learn how to interpret a normal distribution with mean μ = -67.5 and standard deviation σ = 22.4. This problem covers key concepts of statistics, including normal distribution properties. Suitable for high school students in Grades 11-12.

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