Final answer:
To find the expected time for children to clean their rooms in a uniform distribution from 1 to 15 days, use the formula (a + b) / 2. Upon calculation, the expected time is 8 days.
Step-by-step explanation:
The question refers to finding the expected time required for children to clean their rooms, given that the time is uniformly distributed between 1 to 15 days. To find the expected value 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. In this case, a is 1 day and b is 15 days. Substituting these values into the formula gives:
E = (1 + 15) / 2
E = 16 / 2
E = 8 days
Therefore, a parent must expect to wait for 8 days for his children to clean their rooms, which corresponds to option A.