Final answer:
When dealing with a uniform distribution in the interval from one to 15 days, the expected waiting time for children to clean their rooms is calculated as (1+15)/2, which equals 8 days. So, option A, which is 8 days, is the correct answer.
Step-by-step explanation:
The question relates to the topic of probability and statistics within the Mathematics subject, specifically focused on the concept of uniform distribution. In the scenario provided, where the time for children to clean their rooms is uniformly distributed between one to 15 days, the expected waiting time can be calculated using the formula for the mean of a uniform distribution:
The mean (expected value) of a continuous uniform distribution in the interval [a,b] is (a+b)/2. Applying this to the given interval of [1,15] we have:
(1+15)/2 = 16/2 = 8 days
Therefore, a parent can expect to wait for 8 days on average for their children to clean their rooms, which corresponds to option A.