Final answer:
To calculate the probability that X is between two values, shade the region between the two values on a graph and calculate the shaded area of the rectangle.
Step-by-step explanation:
To calculate the probability that X is between two values, shade the region between the two values on a graph and calculate the shaded area of the rectangle. The shaded area represents the probability. For example, to find the probability that x is between 2.3 and 12.7, shade the region between these two values on the graph and calculate the shaded area.
To solve the student's problem, one must use diagrams to identify and shade the correct region representing x. The process typically involves marking the area between two x-values to find probabilities or adjusting for percentiles in a distribution.
To address the student's question regarding finding the unshaded region that represents x, we need a visual representation of the problem provided, which includes diagrams with shaded and unshaded areas. The process would typically involve identifying the relevant portions of the diagram according to the mathematical context, such as probability distributions or functions on a graph.
For example, if we want to find the probability that x is between two values, we would first identify the correct scale on the horizontal axis. Then, we would shade the region between the two x-values given in the problem. If this is a probability distribution, the probability is determined by calculating the area under the curve for the shaded region.
In cases where percentiles are mentioned, like finding the 80th percentile, we would typically modify the diagram to shade the area to the left of this percentile value. Knowing that percentiles divide a distribution into parts, with a certain percentage falling below that value, we adjust the diagram accordingly and use statistical tables or software to find the exact value.