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Consider a StarMetro bus that stops by a particular stop on an hourly basis. An auditing company records the difference between the scheduled time and the actual arrival time. It turns out that the difference between the scheduled time and the actual time denoted by U is uniformly distributed between 3 minutes early and 7 and a half minutes late (I.E. U∼Uniform(-3,7.5)).
What is the probability that the sample mean U ¯ of the 17 recorded differences between actual bus arrivals and scheduled bus arrival times is greater than 3 minutes late?
Suppose you did this process of observing the difference between the actual and scheduled arrival times of 17 busses and then computed the sample mean . What is the 99th percentile of the sample mean U ¯ ?
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