A student has a class that is supposed to end at 9:00 A.M. and another that is supposed to begin at 9:10 A.M. Suppose the actual ending time of the 9 A.M. class is a normally distributed rv X1 with mean 9:02 and standard deviation 1.5 min and that the starting time of the next class is also a normally distributed rv X2 with mean 9:10 and standard deviation 1 min. Suppose also that the time necessary to get from one classroom to the other is a normally distributed rv X3 with mean 6 min and standard deviation 1 min. What is the probability that the student makes it to the second class before the lecture starts? (Assume independence of X1, X2, and X3, which is reasonable if the student pays no attention to the finishing time of the first class.)
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