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The question displayed in the image asks whether the mode of \( X \), where \( X \sim N(3, 25) \), is 25.

Here's a breakdown of the notation and solution:

- \( X \sim N(3, 25) \) means that \( X \) is normally distributed with a mean \( \mu = 3 \) and a variance \( \sigma^2 = 25 \).
- For a normal distribution, the mode, mean, and median all occur at the same value, which is \( \mu \).

Thus, the mode of \( X \) is 3, not 25.

The statement "the mode of \( X \) is 25" is **incorrect**.

Would you like further clarification or details on the normal distribution?

Here are 5 related questions you may find interesting:
1. What is the median of a normal distribution?
2. How do you find the probability for a given interval in a normal distribution?
3. What is the difference between variance and standard deviation in a distribution?
4. How does the mode change in a skewed distribution?
5. Can the mean and mode be different in other types of distributions?

**Tip:** In a normal distribution, the mean, median, and mode are all equal, centered at the peak of the curve.

Learn why the mode of a normal distribution, X ~ N(3, 25), is not 25. This question tests the understanding of normal distribution properties, where the mode equals the mean, μ. Explore how to identify the mode, variance, and mean in such distributions. Suitable for Grades 10-12.

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