Final answer:
To find the area of the shaded region under the standard normal distribution curve, one must calculate the z-scores for the boundaries of the region and then use a z-table or probability calculator to find the cumulative area.
Step-by-step explanation:
The student is asked to find the area of a shaded region under a standard normal distribution curve, which is a graphical representation of the normal distribution of bone density scores with a mean of 0 and a standard deviation of 1. To calculate the area, or the probability, we need to determine the z-scores for the boundaries of the shaded region and then consult the z-table or use probability calculators to find the cumulative area to the left of the z-score. If we need to find the area between two z-scores, we would subtract the area to the left of the lower z-score from the area to the left of the higher z-score.
As an example, to find the area between z-scores of 1 and 2 using a z-table: First, you look up the z-score of 1, which gives an area of approximately 0.8413 to the left of z. Then, look up the z-score of 2, which gives an area of approximately 0.9772. By subtracting the smaller area from the larger, 0.9772 - 0.8413, we find the area of the shaded region is approximately 0.1359 or 13.59%.