Zowee Airline plans to fly several daily flights from Madison to Appleton. Based on historical data, the flight on Wednesday evening before Thanksgiving is always sold out. However, there are usually no-shows so the airline wants to increase revenue by overbooking. They estimate that the no-shows are normally distributed with a mean of 8 and a standard deviation of 2.83. The airline feels that if they “get caught” overbooking, then the cost will be about ten times more than the ticket price. Since Appleton is a family-oriented town, the airline management is dreading bad publicity around Thanksgiving, so it decides that it does not want to bump passengers more than 4% of the time. What is the maximum number of seats the airline should overbook?
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