The Hb level in healthy women has mean 13.5 g/dl and standard detion 1.5 g/dl, what is the Z score for a woman with Hb level 15.0 g/dl:

**Question:** The Hb level in healthy women has a mean of 13.5 g/dl and a standard deviation of 1.5 g/dl. What is the Z score for a woman with Hb level 15.0 g/dl?

**Core Concept:** Z-scores are a way to standardize a measurement by expressing it as a deviation from the mean, allowing comparison across different populations and conditions. In this case, we're calculating a Z score for a woman's hemoglobin (Hb) level based on a normal distribution in healthy women.

**Why the Correct Answer is Right:** In calculating the Z score, we use the following formula:

Z = [(X - μ) / σ]

Where:
- X is the individual measurement (Hb level in this case)
- μ is the mean of the population (13.5 g/dl for healthy women)
- σ is the standard deviation (1.5 g/dl for healthy women)

Applying this formula to the given information:

Z = [(15.0 - 13.5) / 1.5]
Z = [1.5 / 1.5]
Z = 1

**Why Each Wrong Option is Incorrect:** Let's analyze each wrong answer choice:

**Option A**:
Z = [(15.0 - 13.5) / 2.0]
Z = [1.5 / 2.0]
Z = 0.75

**Option B**:
Z = [(15.0 - 13.5) / 2.0]
Z = [1.5 / 2.0]
Z = 0.75

Both options A and B are incorrect because they use the incorrect standard deviation value (2.0 instead of 1.5).

**Option C**:
Z = [(15.0 - 13.5) / 3.0]
Z = [1.5 / 3.0]
Z = 0.5

Option C is incorrect because it uses an incorrect standard deviation value (3.0 instead of 1.5).

**Option D**:
Z = [(15.0 - 13.5) / 1.5]
Z = [1.5 / 1.5]
Z = 1

Option D is correct because it uses the correct standard deviation value (1.5).

**Clinical Pearl**:
Z-scores are useful in comparing measurements across different studies or populations, where the mean and standard deviation are known. They provide a standardized measure of how much a particular measurement deviates from the mean, allowing for comparison between studies. In this example, the correct Z-score for a woman with an Hb level of 15.0 g/dl is 1, which indicates that this Hb level is 1 standard deviation above the mean in healthy women.