Final answer:
The expectation for the time it takes for children to clean their rooms, if this time is uniformly distributed between 1 and 15 days, is found by averaging these two values, resulting in 8 days.
Step-by-step explanation:
The question asks about the expectation of time for children to clean their rooms, which is stated to be uniformly distributed from one to 15 days. The expectation or mean of a uniform distribution can be calculated by taking the average of the minimum and maximum values of the distribution. Therefore, to find this expectation value, we add the minimum time (1 day) and the maximum time (15 days) and divide by 2.
Expectation (mean) = (Minimum time + Maximum time) / 2
Expectation (mean) = (1 day + 15 days) / 2
Expectation (mean) = 16 days / 2
Expectation (mean) = 8 days
The correct answer is A) 8 days. This is the average amount of time a parent can expect to wait for his children to clean their rooms if the days taken to clean are uniformly distributed between 1 and 15 days.