Bob takes a bus everyday to get to his school. The bus takes off exactly at 7.00 everyday. Here is when bob arrives to the bus stop:
day one: 6.58 day two: 6.55 day three: 6.58 day four: 7.02 day five: 7.10
Questions: - What is the probability that bob will be late on the next day? - Would your answer to the first question differ if 7.10 was instead 8.10? - Would your answer to the first question differ if the times on the first and the fifth days were swapped?
Edit: Assume that the data is normally distributed.
My comments: These questions might not have a single definite answer, but I'd still like to see your reasoning. The problem I guess boils down to the following logic question: If bob gets to the stop later day after the day, would it be more logical to expect that bob will be even later on the next time, or will be there approximately somewhere around the mean value. Thanks