To determine the interval of systolic blood pressures that represent the middle 68% of males, we can use the empirical rule (or the 68-95-99.7 rule). This rule states that for a normal distribution:
- Approximately 68% of the data falls within one standard deviation of the mean.
- Approximately 95% of the data falls within two standard deviations of the mean.
- Approximately 99.7% of the data falls within three standard deviations of the mean.
Given that the mean systolic blood pressure for males in this town is 125, and the standard deviation is 5, we need to find the interval within one standard deviation from the mean. This interval will cover the middle 68% of the data.
1. Calculate the lower bound of the interval:
- Subtract the standard deviation from the mean:
[tex]\[
\text{Lower bound} = \text{Mean} - \text{Standard Deviation}
\][/tex]
[tex]\[
\text{Lower bound} = 125 - 5
\][/tex]
[tex]\[
\text{Lower bound} = 120
\][/tex]
2. Calculate the upper bound of the interval:
- Add the standard deviation to the mean:
[tex]\[
\text{Upper bound} = \text{Mean} + \text{Standard Deviation}
\][/tex]
[tex]\[
\text{Upper bound} = 125 + 5
\][/tex]
[tex]\[
\text{Upper bound} = 130
\][/tex]
Therefore, the interval of systolic blood pressures that represent the middle 68% of males is from 120 to 130.
