Final answer:
For a uniformly distributed time interval from one to 15 days for children to clean their rooms, the expected waiting time for a parent is calculated to be 8 days.
Step-by-step explanation:
The question focuses on the cleaning frequency of a dining room tray. Although the cleaning frequency could vary based on different contexts and establishments' guidelines, the related question provided pertains to mathematical probabilities concerning the independent event of children cleaning their rooms.
Using the provided information that cleaning is uniformly distributed within a time interval from one to 15 days, we can calculate the expected value, which is the average time a parent would have to wait. The expected value in a uniform distribution is found by adding the minimum value to the maximum value and dividing by 2. So, we have (1 day + 15 days) / 2 = 16 / 2 = 8 days.