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    Auto Insurance Percentage of Coverage

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    Please help with the following problem.

    An auto insurance company classifies its customers in three categories: poor, satisfactory, and preferred. Each year, 30% of those in the poor category are moved to satisfactory and 5% of those in the satisfactory category are moved to preferred. Also, 5% 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?

    Poor =
    Satisfactory =
    Preferred =

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    Solution Preview

    In the long run, we should expect that the total number in each category remains constant. Let's say that in the long run, there are a poor, b satisfactory and c preferred. We immediately establish the following points,

    -30% of poor goes to satisfactory (poor category becomes 0.7a, satisfactory becomes b+0.3a)

    -5% satisfactory moves to preferred ...

    Solution Summary

    This solution helps with a problem that explains how many customers a company can expect to have in various satisfaction categories.