Final answer:
The expected waiting time for a parent, given that the time to clean rooms is uniformly distributed from 1 to 15 days, is calculated using the expectation formula for uniform distribution and results in 8 days. The correct option is 2.
Step-by-step explanation:
The question pertains to the expectation of time that a parent must wait for his children to clean their rooms, given that the time is uniformly distributed between 1 and 15 days.
To calculate the expected value when dealing with a uniform distribution, you can use the formula E(X) = (a + b) / 2, where 'a' and 'b' are the minimum and maximum values of the distribution, respectively. In this case, 'a' is 1 day and 'b' is 15 days.
Applying the formula, we get E(X) = (1 + 15) / 2 = 16 / 2 = 8. Therefore, the expected waiting time for a parent is 8 days.