Understanding Blood Cholesterol Levels: Z-Scores and Interpretation

Calculating Z-Scores and Blood Cholesterol Levels

Z-Score for Cholesterol Level of 213 mg/dl: To calculate the z-score for a man with a blood cholesterol level of 213 mg/dl, we use the formula z = (X - μ) / σ, where X is the value (213 mg/dl), μ is the mean (181 mg/dl), and σ is the standard deviation (44.5 mg/dl). Plugging in the values, we get z213 = (213 - 181) / 44.5 = 0.7191. Therefore, the z-score for a blood cholesterol level of 213 mg/dl is approximately 0.72.

Blood Cholesterol Level for Z-Score of -1.59: To find the blood cholesterol level corresponding to a z-score of -1.59, we rearrange the formula to solve for X: X = μ + (z * σ), where X is the unknown cholesterol level, μ is the mean (181 mg/dl), z is the z-score (-1.59), and σ is the standard deviation (44.5 mg/dl). Plugging in the values, we have X = 181 + (-1.59 * 44.5) = 111.205 mg/dl. Thus, the blood cholesterol level corresponding to a z-score of -1.59 is approximately 111.21 mg/dl.