Let me analyze the image. One moment please.The question asks for identifying characteristics of a normal distribution. Below are the relevant points based on the given choices:

1. The area under the part of a normal curve that lies within 1 standard deviation of the mean is approximately 0.68: This is correct. For a normal distribution, about 68% of the data falls within 1 standard deviation of the mean.

2. The area under the part of a normal curve that lies within 3 standard deviations of the mean is approximately 0.95: This is incorrect; the correct percentage for within 3 standard deviations is approximately 99.7%. The percentage for 2 standard deviations is approximately 95%.

3. The normal distribution curve is symmetric about the standard deviation: This is incorrect. It is symmetric about the mean, not the standard deviation.

4. The normal distribution curve is unimodal: This is correct. The normal curve has a single peak (one mode).

5. The normal distribution curve crosses the x-axis: This is incorrect. The normal curve approaches, but never touches, the x-axis (it has asymptotic tails).

6. The area under the part of a normal curve that lies within 2 standard deviations of the mean is approximately 0.95: This is correct.

7. The mean, median, and mode are located at the center of the distribution: This is correct. For a normal distribution, these three measures coincide at the center.

8. The total area under the normal distribution curve is 1.00: This is correct. By definition, the total probability for a normal distribution is 1.

9. A normal distribution curve is bell-shaped: This is correct. The standard shape of a normal distribution is bell-shaped.

10. The normal curve is a discrete distribution: This is incorrect. The normal curve represents a continuous distribution, not discrete.

Correct Characteristics:

• The area under the part of a normal curve that lies within 1 standard deviation of the mean is approximately 0.68.
• The normal distribution curve is unimodal.
• The area under the part of a normal curve that lies within 2 standard deviations of the mean is approximately 0.95.
• The mean, median, and mode are located at the center of the distribution.
• The total area under the normal distribution curve is 1.00.
• A normal distribution curve is bell-shaped.

Would you like further explanation about any of these properties?

Relative Questions:

1. Why does the normal distribution curve never touch the x-axis?
2. How do the standard deviation and mean affect the shape of a normal curve?
3. What is the significance of the area under a normal distribution curve?
4. How can the normal distribution be used in real-life data analysis?
5. What are some differences between normal and discrete distributions?

Tip:

Remember, the Empirical Rule (68-95-99.7 Rule) is a quick way to approximate areas under a normal curve within 1, 2, or 3 standard deviations of the mean.