Final answer:
The expected time for children to clean their rooms is calculated by taking the average of the uniform distribution range, which is 8 days.
Step-by-step explanation:
The time it takes for children to clean their rooms is uniformly distributed from 1 to 15 days. To find the expected value (mean) of a uniform distribution, we can use the formula:
Expected value = (a + b) / 2
where 'a' is the minimum value and 'b' is the maximum value. Plugging the numbers in:
Expected value = (1 + 15) / 2
Expected value = 16 / 2
Expected value = 8 days
Therefore, a parent should expect to wait on average 8 days for their children to clean their rooms.