Final answer:
To determine the expected waiting time for a parent when the time for children to clean their rooms is uniformly distributed between 1 and 15 days, use the formula for the expected value of a uniform distribution. The calculation reveals that the parent can expect to wait an average of 8 days.
Step-by-step explanation:
The question concerns the concept of the uniform distribution in probability and statistics, which is part of high school mathematics curriculum. Given that the time it takes for children to clean their rooms is evenly spread out or uniformly distributed between 1 and 15 days, we want to determine the expected waiting time for a parent.
To find the expected value (mean) for a uniform distribution, you can use the formula: Expected value (E) = (a + b) / 2, where 'a' is the minimum value and 'b' is the maximum value of the distribution. Here, 'a' equals 1 day, and 'b' equals 15 days. Substituting these values into the formula gives us E = (1 + 15) / 2 = 16 / 2 = 8.
Thus, the expectation is that a parent will wait for an average of 8 days for their children to clean their rooms.