2. For a medical study, a researcher wishes to select people in the middle 68% of the population
based on blood pressure. If the mean systolic blood pressure is 120 and the standard deviation
is 8, find the upper and lower readings that would qualify people to participate in the study.


This problem involves the **normal distribution**. To find the **middle 68%** of the population based on blood pressure, we will use the **empirical rule**. 

The empirical rule states:
1. 68% of the data in a normal distribution lies within **one standard deviation** of the mean (between \( \mu - \sigma \) and \( \mu + \sigma \)).
2. Therefore, for this study:
   - \( \mu = 120 \) (mean systolic blood pressure)
   - \( \sigma = 8 \) (standard deviation)

### Step-by-Step Solution:
1. **Find the lower boundary:**
   \[
   \text{Lower Bound} = \mu - \sigma = 120 - 8 = 112
   \]

2. **Find the upper boundary:**
   \[
   \text{Upper Bound} = \mu + \sigma = 120 + 8 = 128
   \]

### Answer:
- **Lower reading**: 112
- **Upper reading**: 128

So, people whose systolic blood pressure is between **112 and 128** qualify for the study, as this range captures the middle 68% of the population.

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Would you like further details or a deeper explanation on the concept of standard deviations or the empirical rule?

### 5 Related Questions:
1. What is the empirical rule, and how does it apply to different percentages (95%, 99.7%)?
2. How would the selection criteria change if the study focused on the middle 95%?
3. Can you explain how to compute probabilities using the Z-table for non-standard distributions?
4. What are outliers in a normal distribution, and how are they identified?
5. How does changing the standard deviation affect the qualifying range?

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**Tip**: When working with the normal distribution, always double-check if the problem refers to standard deviations directly or if it needs a Z-score calculation for non-standard intervals.

For a medical study, a researcher wishes to select people in the middle 68% of the population based on blood pressure. If the mean systolic blood pressure is 120 and the standard deviation is 8, find the upper and lower readings that would qualify people to participate in the study.

Discover how to calculate the blood pressure range for the middle 68% of the population using the normal distribution. This example uses a mean of 120 and a standard deviation of 8, with the empirical rule to determine the upper and lower limits. Perfect for high school students studying statistics.

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