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The question in the image is as follows:

> On a certain intelligence test, the mean is 70, with a standard deviation of 11. The results come very close to fitting a normal curve. Suppose this test is given to a very large group of people. Use the empirical rule to find the percentage of people whose test scores are more than 70.

### Solution

Since the distribution of scores is approximately normal, we can use the empirical rule (also known as the 68-95-99.7 rule), which states:
- **68%** of data falls within **1 standard deviation** of the mean.
- **95%** of data falls within **2 standard deviations** of the mean.
- **99.7%** of data falls within **3 standard deviations** of the mean.

Given:
- Mean \( \mu = 70 \)
- Standard deviation \( \sigma = 11 \)

We are asked for the percentage of people scoring **more than 70**. Since the mean is 70, this is the point where the distribution splits in half. Therefore:
- **50%** of the population scores more than the mean of 70 in a normal distribution.

### Answer
The percentage of people whose test scores are more than 70 is **50%**.

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Would you like more details on the empirical rule or further examples?

Here are some additional related questions:
1. What percentage of people score between 59 and 81 on this test?
2. What percentage of people score below 59?
3. What is the probability of a person scoring more than 92 on this test?
4. How would the percentage change if the mean were adjusted to 75 with the same standard deviation?
5. How does the empirical rule help estimate probabilities in a normal distribution?

**Tip:** The empirical rule is particularly useful when data is normally distributed, providing quick estimates without needing exact calculations.

On a certain intelligence test, the mean is 70, with a standard deviation of 11. The results come very close to fitting a normal curve. Suppose this test is given to a very large group of people. Use the empirical rule to find the percentage of people whose test scores are more than 70.

Learn how to use the empirical rule to find the percentage of people scoring above the mean on a normal distribution. This problem involves calculating the percentage of test scores above the mean of 70 with a standard deviation of 11.

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