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

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

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Please find the percentage of poor, satisfactory, and preferred

An auto insurance company classifies its customers in three categories: poor, satisfactory, and preferred. Each year, 5% of those in the poor category 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? Poor = % (Round to the nearest tenth if necessary.)
Transcribed Image Text:An auto insurance company classifies its customers in three categories: poor, satisfactory, and preferred. Each year, 5% of those in the poor category 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? Poor = % (Round to the nearest tenth if necessary.)
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