Final answer:
The area of a shaded region in a normal distribution graph represents the probability between two x-values and is found using z-scores and the mean and standard deviation. Areas under the curve can be calculated with the sum of the areas of geometric shapes, and percentiles correspond to certain areas under the normal curve.
Step-by-step explanation:
The area of the shaded region in a graph that represents normal distribution can be calculated by using the properties of the normal curve. When given particular x-values and the mean and standard deviation of the distribution, you can find the corresponding area under the curve, which represents probability. If the task is to find the area between two values (e.g., x = 2.3 and x = 12.7) on a normal distribution with a known mean and standard deviation, you would typically utilize a z-score table or statistical software to find the probability that a score falls between these two values.
In a scenario where one must calculate the final displacement by the area under a graph, this involves summing up geometric shapes such as rectangles and triangles. For example, if a graph has shaded regions that represent a rectangle and a triangle, you would separately calculate the area of the rectangle (base times height) and the area of the triangle (0.5 times base times height) and then add these areas together.
When looking for a percentile, such as the 90th percentile, in a normal distribution, you would find the z-score that corresponds to an area of 0.9 to the left of the z-score on the curve. You can then translate this z-score back to the original scale using the mean and standard deviation to find the actual score that represents the 90th percentile.