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The problem asks to use the empirical rule to find the percentage of people whose test scores are between 55 and 145, given a mean score of 100 and a standard deviation of 15.

### Solution:

The **empirical rule** (also known as the 68-95-99.7 rule) for a normal distribution states that:
1. 68% of data lies within 1 standard deviation from the mean.
2. 95% of data lies within 2 standard deviations from the mean.
3. 99.7% of data lies within 3 standard deviations from the mean.

Here, the mean (μ) is 100, and the standard deviation (σ) is 15.

We need to find the percentage of people whose scores fall between **55** and **145**.

- **Lower bound**: 55
  - This is (55 - 100) / 15 = -3 standard deviations from the mean.

- **Upper bound**: 145
  - This is (145 - 100) / 15 = +3 standard deviations from the mean.

So, 55 to 145 represents data that is within **3 standard deviations** from the mean. According to the empirical rule, **99.7%** of the data lies within 3 standard deviations of the mean.

### Final Answer:
The percentage of people whose scores are between 55 and 145 is **99.7%**.

Would you like more details or have any other questions?

Here are 5 related questions:
1. How do we use the empirical rule to find values within 1 or 2 standard deviations?
2. What is the probability of a score being more than 3 standard deviations from the mean?
3. Can the empirical rule be applied to non-normal distributions?
4. How would the answer change if the standard deviation was different?
5. What is the relationship between the empirical rule and the z-score?

**Tip:** The empirical rule is a quick approximation for normal distributions, but for precise results, statistical software or z-tables can be used to calculate exact percentages.

On a certain test, the mean is 100 with a standard deviation of 15. What is the percentage of people whose test scores are between 55 and 145?

Use the empirical rule to determine the percentage of people whose test scores are between 55 and 145, with a mean of 100 and a standard deviation of 15. This problem focuses on normal distribution and the 68-95-99.7 rule.

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