Which of the following option is/are correct?

For a standard normal density curve, the value of standard deviation is 1.

Normal distribution is also known as Gaussian distribution.

In Normal distribution, the highest value of its density occurs at mean.

The width of the normal density curve increase as its standard deviation increase.

Let's analyze each of the given statements to determine which are correct.

### Statement 1: For a standard normal density curve, the value of standard deviation is 1.

- **Explanation**: A standard normal distribution is a special case of the normal distribution with a mean of 0 and a standard deviation of 1.
- **Correctness**: This statement is **correct**.

### Statement 2: Normal distribution is also known as Gaussian distribution.

- **Explanation**: The normal distribution is indeed often referred to as the Gaussian distribution, named after the mathematician Carl Friedrich Gauss.
- **Correctness**: This statement is **correct**.

### Statement 3: In Normal distribution, the highest value of its density occurs at mean.

- **Explanation**: For a normal distribution, the probability density function is symmetric about the mean, and the highest point (the peak) of the curve occurs at the mean.
- **Correctness**: This statement is **correct**.

### Statement 4: The width of the normal density curve increases as its standard deviation increases.

- **Explanation**: The standard deviation determines the spread or width of the normal distribution. A larger standard deviation means that the curve is wider and more spread out, while a smaller standard deviation means the curve is narrower.
- **Correctness**: This statement is **correct**.

### Conclusion
All the given statements are correct:

1. The standard deviation of the standard normal distribution is 1.
2. The normal distribution is also known as the Gaussian distribution.
3. The highest value of the density function occurs at the mean.
4. The width of the normal density curve increases as the standard deviation increases.

Would you like to explore more details or ask any questions? Here are five related questions you might find interesting:

1. How does the standard normal distribution differ from other normal distributions?
2. What is the significance of the mean and standard deviation in determining the shape of a normal distribution?
3. How would you calculate probabilities using the standard normal distribution?
4. Can you explain why the normal distribution is considered a continuous probability distribution?
5. How does the empirical rule (68-95-99.7) relate to the standard normal distribution?

**Tip:** Visualizing the normal distribution curve and understanding its properties can greatly aid in grasping concepts related to probability and statistics.

Explore the properties of normal distribution and standard deviation with detailed explanations. Learn about the standard normal density curve, Gaussian distribution, density function peaks at mean, and the relationship between standard deviation and curve width.

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