Suppose your waiting time (in minutes) for a bus in the morning is uniformly distributed on [0,10]. Suppose you take the bus each morning for a total of 200 days in an academic year and denote the average waiting time of these 200 days as X.

1. What is your expected value of your average waiting time?
2. What is the variance of your average waiting time?
3. Apply CLT (central limit theorem) to approximately calculate the probability that your average waiting time exceeds 8 minutes.
4. What is the probability that your average waiting time exceeds 8 minutes.
5. Compare 3) and 4) and explain the difference.