Chapter 9.2, Problem 4MP

A mail-order company classifies its customers as preferred, standard, or infrequent depending on the number of orders placed in a year. Past records indicate that each year, $5\%$ of preferred customers are reclassified as standard and $12\%$ as infrequent, $5\%$ of standard customers are reclassified as preferred and $5\%$ as infrequent, and $9\%$ of infrequent customers are reclassified as preferred and $10\%$ as standard. Assuming that these percentages remain valid, what percentage of customers are expected to be in each category in the long run?