Question

A master cleaning schedule should be reviewed for updates

A. Every month
B. Every quarter
C. Every year
D. As needed

Answer 1

The expected wait time for children to clean their rooms, given a uniform distribution of 1 to 15 days, is 8 days. This is calculated by finding the average of the lowest and highest values in the range.

Step-by-step explanation:

The question is asking how long a parent should expect to wait for his children to clean their rooms if the time it takes is uniformly distributed from one day to fifteen days. In a uniform distribution, the expected value or mean is calculated by adding the lowest value in the range to the highest value and then dividing by two.

To calculate this: (1 day + 15 days) / 2 = 16 / 2 = 8 days. Therefore, the parent can expect that on average, it will take 8 days for the children to clean their rooms. This represents the midpoint of the time interval, which is the average wait time in a uniformly distributed data set.

Answer 2

The student asked a mathematics question specific to the expected value of a uniform distribution. The correct answer is A. 8 days, as it is the average of the uniform distribution range from 1 to 15 days for kids cleaning their rooms.

Step-by-step explanation:

The question involves calculating the expected value of a uniformly distributed continuous random variable, which measures the average outcome if an experiment is repeated many times. In this case, the time interval for children to clean their rooms is uniformly distributed between 1 and 15 days. To find the expected value (mean) of a uniform distribution, we use the formula:

Expected value (E[X]) = (a + b) / 2

Where a is the minimum value and b is the maximum value. Let's apply this to the given data:

E[X] = (1 + 15) / 2

E[X] = 16 / 2

E[X] = 8 days

Therefore, a parent must expect to wait for 8 days on average for his children to clean their rooms, which corresponds to option