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The problem asks to determine the interval of systolic blood pressures that represents the middle 99.7% of males, given that systolic blood pressure is normally distributed with a mean of 105 and a standard deviation of 10.

To solve this, we can use the empirical rule, which states that:

- **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.

Since we are asked to find the interval that represents the middle 99.7%, we are interested in the range that falls within **3 standard deviations** of the mean.

### Calculation:

1. **Mean (μ) = 105**
2. **Standard deviation (σ) = 10**

The interval can be found by calculating \( \mu \pm 3\sigma \):

\[
\text{Lower bound} = 105 - 3(10) = 105 - 30 = 75
\]
\[
\text{Upper bound} = 105 + 3(10) = 105 + 30 = 135
\]

### Final answer:
The interval of systolic blood pressures that represents the middle 99.7% of males is **75 to 135**.

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Do you have any questions or would you like further details?

Here are some related questions for practice:

1. What is the interval for the middle 95% of systolic blood pressures?
2. How much of the data falls outside the interval for the middle 99.7%?
3. How does the empirical rule differ from Chebyshev's inequality?
4. How would the interval change if the standard deviation increased to 15?
5. What interval would represent the middle 68% of systolic blood pressures?

**Tip:** The empirical rule applies best to bell-shaped, normal distributions. Always check if the data distribution is approximately normal before applying this rule.

For males in a certain town, the systolic blood pressure is normally distributed with a mean of 105 and a standard deviation of 10. Using the empirical rule, determine the interval of systolic blood pressures that represent the middle 99.7% of males.

Learn how to calculate the interval for the middle 99.7% of systolic blood pressures using the empirical rule. With a mean of 105 and a standard deviation of 10, this problem demonstrates key statistical concepts related to normal distribution and the 68-95-99.7 rule.

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