Let's analyze the image to address the question on the characteristics of a normal distribution.

The characteristics of a normal distribution include the following correct points:

1. The normal distribution curve is unimodal.

   • A normal distribution has one peak, which means it is unimodal.

2. The area under the part of a normal curve that lies within 3 standard deviations of the mean is approximately 0.95.

   • Incorrect. This is slightly off. The area within 3 standard deviations is approximately 99.7%, not 95%. Instead, 95% lies within 2 standard deviations.

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

   • Correct. This is consistent with the empirical rule (68-95-99.7 rule).

4. The total area under the normal distribution curve is 1.00.

   • Correct. This is a defining property of probability distributions.

5. The normal distribution curve crosses the x-axis.

   • Correct. Although it approaches the x-axis asymptotically, it never actually touches or crosses it.

6. The mean, median, and mode are located at the center of the distribution.

   • Correct. In a normal distribution, these three measures of central tendency are the same and located at the peak.

7. The area under the part of a normal curve that lies within 1 standard deviation of the mean is approximately 0.68.

   • Correct. Again, consistent with the empirical rule.

8. The normal distribution curve is symmetric about the standard deviation.

   • Incorrect. The curve is symmetric about the mean, not the standard deviation.

9. The normal curve is a discrete distribution.

   • Incorrect. A normal distribution is continuous, not discrete.

10. A normal distribution curve is bell-shaped.

• Correct. This is one of its primary characteristics.

Final Correct Answers:

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

Let me know if you'd like detailed explanations or have more questions!

5 Relative Questions:

1. What is the empirical rule, and how is it applied to normal distributions?
2. Why is the total area under a probability distribution curve always 1?
3. What distinguishes a continuous distribution from a discrete distribution?
4. How can we verify if a given dataset approximates a normal distribution?
5. What are some real-world examples of phenomena that follow a normal distribution?

Tip:

When working with normal distributions, remember the empirical rule (68-95-99.7), which makes quick probability estimates easier!