For males in a certain town, the systolic blood pressure is normally distributed with a mean of 135 and a standard deviation of 5 Using the empirical rule, determine the interval of systolic blood pressures that represent the middle 99.7of males.
The empirical rule states that for a normal distribution:
- Approximately 68% of the data falls within 1 standard deviation of the mean
- Approximately 95% of the data falls within 2 standard deviations of the mean
- Approximately 99.7% of the data falls within 3 standard deviations of the mean
Since the mean systolic blood pressure is 135 and the standard deviation is 5, we can calculate the interval that represents the middle 99.7% of males by adding and subtracting 3 standard deviations from the mean:
Lower limit = 135 - 3(5) = 135 - 15 = 120
Upper limit = 135 + 3(5) = 135 + 15 = 150
Therefore, the interval of systolic blood pressures that represent the middle 99.7% of males in this town is 120 to 150.