Final answer:
To find the expected time for children to clean their rooms, which is uniformly distributed between 1 and 15 days, calculate the average (1 day + 15 days) / 2, which equals 8 days. Therefore, the parent can expect to wait on average 8 days.
Step-by-step explanation:
The problem presented is one concerning the uniform distribution of a random variable, which in this case is the time taken by children to clean their rooms. When a variable is uniformly distributed between two values, the expected value can be calculated as the average of the two extremes. In this case, the time interval is from 1 to 15 days.
To find the expected value (average time), we use the formula for the average of a uniform distribution: (a + b) / 2, where 'a' is the minimum value and 'b' is the maximum value.
The computation would be:
(1 day + 15 days) / 2 = 16 days / 2 = 8 days.
So the parent can expect to wait for an average of 8 days for their children to clean their rooms, making option A the correct answer.