**Core Concept**
The Z score is a measure of how many standard deviations an individual value is away from the mean in a normal distribution. It is calculated using the formula: Z = (X - μ) / σ, where X is the individual value, μ is the mean, and σ is the standard deviation.
**Why the Correct Answer is Right**
To calculate the Z score for the woman with a hemoglobin (Hb) level of 16.5 g/dl, we use the given mean (μ = 13.5 g/dl) and standard deviation (σ = 1.5 g/dl). Plugging these values into the formula, we get: Z = (16.5 - 13.5) / 1.5 = 3 / 1.5 = 2. This means that the woman's Hb level is 2 standard deviations above the mean.
**Why Each Wrong Option is Incorrect**
**Option A:** This option is incorrect because it does not provide a valid calculation for the Z score. Without a correct calculation, it is impossible to determine its accuracy.
**Option B:** This option is incorrect because it does not take into account the correct calculation for the Z score. A Z score of 0 would indicate that the woman's Hb level is equal to the mean, which is not the case here.
**Option C:** This option is incorrect because it is a negative value, which would indicate that the woman's Hb level is below the mean. However, we know that her Hb level is above the mean.
**Clinical Pearl / High-Yield Fact**
When calculating Z scores, it is essential to use the correct formula and to ensure that the units are consistent. A Z score can be used to compare an individual's value to the mean of a population, which can be useful in various clinical and research settings.
**Correct Answer: C. -2**
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