Suppose your waiting time (in minutes) for a bus in the morning is uniformly distributed on [0,10].
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Question:
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.
- What is your expected value of your average waiting time?
- What is the variance of your average waiting time?
- Apply CLT (central limit theorem) to approximately calculate the probability that your average waiting time exceeds 8 minutes.
- What is the probability that your average waiting time exceeds 8 minutes.
- Compare 3) and 4) and explain the difference.
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