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The question asks you to use the empirical rule (also known as the 68-95-99.7 rule) to solve a problem regarding the distribution of systolic blood pressure among 18-year-old women. Here's how we can break it down:

### Given:
- Mean systolic blood pressure, \(\mu = 120 \text{ mmHg}\)
- Standard deviation, \(\sigma = 12 \text{ mmHg}\)
- You are asked to find the percentage of 18-year-old women with systolic blood pressure between **96 mmHg** and **144 mmHg**.

### Solution using the Empirical Rule:
The empirical rule states the following for a normal distribution:
- 68% of the data falls within 1 standard deviation of the mean.
- 95% of the data falls within 2 standard deviations of the mean.
- 99.7% of the data falls within 3 standard deviations of the mean.

#### Step 1: Calculate the number of standard deviations from the mean.
- For 96 mmHg: 
  \[
  Z = \frac{96 - 120}{12} = \frac{-24}{12} = -2 \quad \text{(i.e., 2 standard deviations below the mean)}
  \]
- For 144 mmHg: 
  \[
  Z = \frac{144 - 120}{12} = \frac{24}{12} = 2 \quad \text{(i.e., 2 standard deviations above the mean)}
  \]

#### Step 2: Apply the empirical rule.
Since 96 mmHg and 144 mmHg are 2 standard deviations away from the mean, we use the part of the empirical rule that tells us that **95%** of the data falls within 2 standard deviations of the mean.

### Answer:
Therefore, **95%** of 18-year-old women will have a systolic blood pressure between 96 mmHg and 144 mmHg.

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Would you like more details or have any other questions on this?

Here are 5 related questions to expand your understanding:
1. What percentage of women have systolic blood pressure below 96 mmHg?
2. What percentage of women have systolic blood pressure above 144 mmHg?
3. How would the percentage change if the range were between 108 mmHg and 132 mmHg?
4. How is the empirical rule different from using z-scores and a normal distribution table?
5. Can the empirical rule be applied to any kind of data distribution?

**Tip:** The empirical rule only applies to data that is approximately normally distributed, so make sure to check the distribution before using it.

The systolic blood pressure of 18-year-old women is normally distributed with a mean of 120 mmHg and a standard deviation of 12 mmHg. What percentage of 18-year-old women have systolic blood pressure between 96 mmHg and 144 mmHg?

Learn how to calculate the percentage of 18-year-old women with systolic blood pressure between 96 and 144 mmHg using the empirical rule. This problem involves normal distribution and statistical analysis, perfect for high school students.

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