The Iron Chicken restaurant is located on a busy interstate highway. Most of its customers are just

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The Iron Chicken restaurant is located on a busy interstate highway. Most of its customers are just passing through and will never return to the Iron Chicken. But some are truck drivers whose routes take them past the Iron Chicken on a regular basis. Sybil, the nearsighted waitress at the Iron Chicken is unable to distinguish regular customers from one-time customers. Sybil can either give a customer good service or bad service. She knows that if she gives bad service to any customer, then she will get a small tip. If she gives good service to a truck driver, he will give her a large tip in the (futile) hope that she will recognize him the next time he comes, but if she gives good service to a one-time customer, he will still leave a small tip. Suppose that the cost to Sybil of giving a customer good service rather than bad service is $1. The tips given by dissatisfied customers and customers just passing through average $0.50 per customer. A truck driver who has received good service and plans to come back will leave a tip of $2. Sybil believes that the fraction of her customers who are truck drivers who plan to come back is x. In equilibrium we would expect Sybil to give good service if x is greater than __________ and bad service if x is smaller.

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