Final answer:
The question revolves around interpreting systolic blood pressure readings using statistical methods within the Mathematics field, appropriate for the College level. It involves understanding concepts like histograms, normal distribution, means, standard deviations, and z-scores.
Step-by-step explanation:
The subject of the question is Mathematics, specifically statistics as it pertains to the study of systolic blood pressure readings and their distribution among a population. The grade level is College, given the complexity of the statistical analysis required for interpreting blood pressure data and understanding histograms, normal distributions, and z-scores.
Systolic blood pressure is a measure of the pressure in the arteries when the heart beats and is recorded as the higher number in a blood pressure reading. The typical blood pressure of a young adult is around 120 mm Hg systolic. A normal distribution of systolic blood pressure for a specific age range is an important aspect in health science research. To calculate z-scores for systolic blood pressure readings:
- Subtract the mean from the blood pressure reading.
- Divide the result by the standard deviation.
For example, for a male with a mean systolic blood pressure (μ) of 125 mm Hg and a standard deviation (σ) of 14 mm Hg:
- The z-score for a blood pressure of 100 mm Hg is (100 - 125) / 14 = -1.79.
- The z-score for a blood pressure of 150 mm Hg is (150 - 125) / 14 = 1.79.
Given that z-scores represent the number of standard deviations a value is from the mean, if your friend believes his systolic blood pressure is 2.5 standard deviations below the mean, you would tell him that his blood pressure should be around 125 - (2.5 x 14) = 90 mm Hg, which is not between 100 and 150 millimeters.