Final answer:
The area of the shaded region in a standard normal distribution represents the probability of a bone density score falling in that region. It's calculated by looking up the z-scores of the region's cut-off scores in standard normal distribution tables. The procedure varies some depending on the location of the shaded region.
Step-by-step explanation:
The area of the shaded region in a standard normal distribution graph represents the probability of a bone density score falling within that region. The mean of 0 and standard deviation of 1 inform us that this distribution is standardized.
To find the area, we need to look up the z-score, corresponding to the cut-off points of the shaded region, in standard normal distribution tables.
If the z-scores corresponding to the cut-off points aren't provided, you would typically calculate them using the formula Z = (X - μ)/σ, where X is the cut-off point, μ is the mean of the distribution, and σ is the standard deviation. But since this distribution is standardized, the mean is 0 and the standard deviation is 1, so the cut-off scores themselves are also the z-scores.
It is important to note that the exact procedure might change based on the location of the shaded region: left tail, right tail, or in between two scores.
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