**Core Concept:** Z-score is a statistical method used to standardize the measurement of an individual's value relative to a population mean and standard deviation. In this case, we are calculating the Z-score for hemoglobin (Hb) levels in women.
**Why the Correct Answer is Right:**
The Z-score for a woman with a hemoglobin level of 15 g/dl can be calculated using the following formula:
Z = [(X - ΞΌ) / Ο]
Where:
- X is the individual's measurement (15 g/dl)
- ΞΌ is the population mean (13.5 g/dl)
- Ο is the population standard deviation (1.5 g/dl)
Plugging these values into the formula, we get:
Z = [(15 - 13.5) / 1.5] = 1.2
**Why Each Wrong Option is Incorrect:**
A. The formula is correct, but the interpretation is incorrect. A Z-score of 1.2 suggests that the woman's hemoglobin level is 1.2 standard deviations higher than the mean.
B. Incorrect calculation or interpretation of Z-score.
C. The formula is correct, but the interpretation is incorrect. A Z-score of 1.2 suggests that the woman's hemoglobin level is 1.2 standard deviations higher than the mean.
D. Incorrect calculation or interpretation of Z-score.
**Why the Correct Answer is Right:**
A woman with a hemoglobin level of 15 g/dl has a Z-score of 1.2. This indicates that her hemoglobin level is 1.2 standard deviations higher than the mean, which is clinically significant because it suggests an elevated hemoglobin level in comparison to the normal range for women.
**Clinical Pearl:** Hemoglobin levels above 14 g/dl in women may indicate iron deficiency anemia, polycythemia, or other underlying causes. A thorough clinical evaluation and additional investigations are necessary to determine the cause of elevated hemoglobin levels in women.
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