To find the percentage of patients who had waiting times in the class interval $25 < x \leq 30$ out of those in the class interval $20 < x \leq 30$, we can use the given data from both tables.

1. From the first table, the frequency for the interval $20 < x \leq 30$ is 15.
2. From the second table, the frequency for the interval $25 < x \leq 30$ is 12.

Now, to calculate the percentage of patients in the interval $25 < x \leq 30$ from those in the interval $20 < x \leq 30$, we use the formula:

$\text{Percentage} = \left( \frac{\text{Frequency of } 25 < x \leq 30}{\text{Frequency of } 20 < x \leq 30} \right) \times 100$

$\text{Percentage} = \left( \frac{12}{15} \right) \times 100 = 80\%$

So, 80% of the patients who had waiting times in the interval $20 < x \leq 30$ also had waiting times in the interval $25 < x \leq 30$.

Would you like more details on this, or do you have any questions? Here are 5 follow-up questions to think about:

1. How would the percentage change if the interval was split further?
2. Can you calculate the percentage of patients who waited less than 15 minutes using the second table?
3. What is the total number of patients surveyed according to the data?
4. How would you visualize this data in a bar chart?
5. How could the average waiting time be estimated from these frequency tables?

Tip: When working with percentages in class intervals, always ensure you're comparing the correct intervals and frequencies to avoid mistakes.