https://file.aiquickdraw.com/mathbot/file/1726793171331qvf7scxz.jpg

The question asks to apply the **Empirical Rule** to determine the percentage of 18-year-old women who have a systolic blood pressure **less than 144 mmHg**.

### Given Information:
- **Mean**: 120 mmHg
- **Standard Deviation (σ)**: 12 mmHg
- **Target**: Systolic blood pressure **less than 144 mmHg**.

### The Empirical Rule (68-95-99.7 Rule):
- **68%** of the data lies within 1 standard deviation of the mean.
- **95%** of the data lies within 2 standard deviations.
- **99.7%** of the data lies within 3 standard deviations.

### Step-by-Step Solution:

1. **Calculate how far 144 mmHg is from the mean**:
   - \(144 - 120 = 24\) mmHg.
   
2. **Determine how many standard deviations 144 is from the mean**:
   - \( \frac{24}{12} = 2 \) standard deviations.

3. **Interpret using the Empirical Rule**:
   - According to the Empirical Rule, **95%** of the population lies within 2 standard deviations of the mean (from 96 mmHg to 144 mmHg).
   - Since the distribution is symmetric, half of the data (47.5%) is below the mean and the other half (47.5%) is above the mean within 2 standard deviations.

4. **Conclusion**: 
   - Therefore, **97.5%** (50% + 47.5%) of 18-year-old women have systolic blood pressure **less than 144 mmHg**.

Let me know if you would like more details!

Here are 5 related questions for practice:
1. What percentage of the population has systolic blood pressure between 108 mmHg and 132 mmHg?
2. What percentage of women have a systolic blood pressure greater than 144 mmHg?
3. If systolic blood pressure is 96 mmHg, how many standard deviations below the mean is it?
4. What is the range of blood pressures that contain 68% of the population?
5. How does the Empirical Rule apply to non-normal distributions?

**Tip**: The Empirical Rule only applies to normal (bell-shaped) distributions. Always check if the data follows this pattern!

The distribution of systolic blood pressures for 18-year-old women is bell shaped with a mean of 120 mmHg and a standard deviation of 12. According to the Empirical rule, what percentage of 18-year-old women have a systolic blood pressure less than 144 mmHg?

Explore how the Empirical Rule is used to calculate that 97.5% of 18-year-old women have systolic blood pressures less than 144 mmHg, based on a normal distribution with a mean of 120 mmHg and standard deviation of 12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation