the organizers of the red maple college fun run gathered data about the runners ages. this box plot shows…

Explanation:

Step1: Recall box - plot properties

In a box - plot, the box represents the inter - quartile range (IQR), which contains 50% of the data. The lower quartile ($Q_1$) is at the start of the box and the upper quartile ($Q_3$) is at the end of the box. The median is the line inside the box. Also, the whiskers represent the rest of the data.

Step2: Identify quartile values from the box - plot

Assume the box - plot has the following properties: The lower end of the box is at 25 (which is $Q_1$) and the upper end of the box is at 45 (which is $Q_3$). We want to find the percentage of data between 20 and 45. Since 20 is below $Q_1$ and 45 is $Q_3$, we know that from $Q_1$ to $Q_3$ is 50% of the data. Also, we need to consider the data from 20 to 25. Since the data from the start of the lower whisker to $Q_1$ is 25% of the data. If we assume a relatively even distribution in the lower 25% of the data, we note that the distance from 15 (assumed lower - whisker start) to 25 ($Q_1$) is 10 units and the distance from 20 to 25 is 5 units. So the percentage of data from 20 to 25 is $\frac{5}{10}\times25% = 12.5%$.

Step3: Calculate the total percentage

The percentage of data from 20 to 45 is the sum of the percentage from 20 to 25 and the percentage from 25 to 45. The percentage from 25 to 45 is 50% and the percentage from 20 to 25 is 12.5%. So the total percentage is $12.5%+50% = 62.5%$.

Answer:

62.5