Final answer:
To find the average time a parent must wait for children to clean their rooms, given the time is uniformly distributed between 1 and 15 days, we use the mean formula of a uniform distribution to get (1 day + 15 days) / 2, which equals 8 days.
Step-by-step explanation:
The question pertains to the average time it takes for a random event to occur, which is represented as a uniform distribution in a probability or statistics context. When the length of time for children to clean their rooms is uniformly distributed between one and 15 days, the average or expected time can be calculated using the formula for the uniform distribution's mean, which is (a + b) / 2. Here, 'a' is the minimum time (1 day) and 'b' is the maximum time (15 days).
Applying the formula, we get:
Average time = (1 day + 15 days) / 2
Average time = 16 days / 2
Average time = 8 days
Therefore, the parent can expect to wait an average of 8 days for his children to clean their rooms, which corresponds to option A.