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an auto insurance company classifies its customers in three catagories; poor, satisfactory and preferred. Each year, 35% of those in the poor catagory are moved to satisfactory and 20% of those in the satisfactory category are moved to preferred. Also, 20% in the preferred category are moved to the satisfactory category, and 20% of those in the satisfactory category are moved to the poor category. Customers are never moved from poor to preferred, or conversely, in a single year. Assuming these percentages remain valid over a long period of time, how many customers can the company expect to have in each category in the long run?
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