Problem 3. Northeastern Runs on Dunkin' (10 points) You may have seen that the Shillman Hall Dunkin' recently announced extended hours. This had me thinking about how long most locations stay open. Of the 10 closest stores to Northeastern, three are open for 8 hours on Tuesdays, two are open for 13 hours on Tuesdays, and one store is open for 7.5,6,14.5,11, and 7 hours each on Tuesdays, respectively. Consider an experiment where you select a single one of these stores uniformly. State the probability distribution over the number of hours the selected store is open. What is the expected value, variance and standard deviation of the number of hours the selected store is open on Tuesdays? Show your work