(Solution) - A class of 40 students is supposed to arrive at -(2025 Original AI-Free Solution)

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A class of 40 students is supposed to arrive at 8:30 AM, but in practice they each arrive at a time uniformly distributed between 8:20 AM and 8:35 AM, and their arrival times are independent.
a. What is the expected arrival time of the last student to arrive?
b. What is the probability that 38 or more of the students have arrived by 8:30 AM?