Looking at the graph of the normal distribution, here is the interpretation:

• a. The mean:
  The mean of a normal distribution is the value at the peak of the curve. From the graph, the peak appears to be centered at 83.

• b. The median:
  For a normal distribution, the mean, median, and mode are the same because the distribution is symmetric. Therefore, the median is also 83.

• c. The mode:
  Similarly, the mode is the value that appears most frequently, which corresponds to the peak of the curve. Thus, the mode is also 83.

• d. The standard deviation:
  The standard deviation can be estimated by looking at the distance between the mean (83) and the points of inflection, where the curve changes from concave up to concave down. From the graph, it looks like one standard deviation from the mean is approximately the distance from 83 to about 11 units (either side: 72 or 94), so the standard deviation is approximately 11.

To summarize:

• Mean = 83
• Median = 83
• Mode = 83
• Standard deviation ≈ 11

Would you like more details or have any other questions?

Here are five related questions:

1. How can we calculate the exact standard deviation using data?
2. What are the properties of a normal distribution?
3. How is the empirical rule (68-95-99.7) used with standard deviations in a normal curve?
4. Why are the mean, median, and mode the same in a normal distribution?
5. How would the graph change if the standard deviation were larger?

Tip: The area under the normal distribution curve always represents 100% of the data. The shape and spread of the curve are controlled by the mean and standard deviation.