Final answer:
The systolic blood pressure is normally distributed with known mean and standard deviation. Z-scores can be calculated using the formula (X - μ) / σ. For example, a blood pressure of 100 mmHg corresponds to a z-score of approximately -1.79.
Step-by-step explanation:
The probability distribution of X, the systolic blood pressure, is a normal distribution with the parameters μ (mean) and σ (standard deviation). So, for the given information, X has a mean (μ) of 120 mmHg and a standard deviation (σ) of 28.2 mmHg.
To calculate the z-scores for systolic blood pressures 100 and 150 millimeters, you would use the formula:
Z = (X - μ) / σ
- For X = 100 mmHg, Z = (100 - 125) / 14 ≈ -1.79
- For X = 150 mmHg, Z = (150 - 125) / 14 ≈ 1.79
If someone thought his systolic blood pressure was 2.5 standard deviations below the mean, and his blood pressure was between 100 and 150 millimeters, this would not be possible because 2.5 standard deviations below the mean of 125 mmHg would be 95 mmHg (125 - 2.5*14).
If Kyle's doctor tells him that the z-score for his systolic blood pressure is 1.75, then Kyle's systolic blood pressure is 1.75 standard deviations above the mean, which translates to a specific value calculated as follows:
X = μ + Z*σ
X = 125 + 1.75*14 ≈ 149.5 mmHg