Final answer:
To calculate the expected wait time for children to clean their rooms when the time is uniformly distributed between 1 to 15 days, use the formula for the mean of a uniform distribution. The calculated expected wait time is 8 days, which is answer choice A.
Step-by-step explanation:
The question being addressed relates to the expectation of how long a parent must wait for their children to clean their rooms, given the period is uniformly distributed between one and 15 days. To find the expected value in a uniform distribution, you calculate the average of the maximum and minimum values. The formula for the expected value or mean (μ) of a uniform distribution is μ = (a + b) / 2, where 'a' is the minimum value, and 'b' is the maximum value.
In this scenario, the minimum time is one day and the maximum time is 15 days. Therefore, the expected wait time is (1 + 15) / 2 which is 16 / 2, resulting in an expected wait time of 8 days. Thus, the correct answer is A. 8 days.