Offwefly Airlines has a daily flight from Sacramento to Las Vegas with a capacity of 100 passengers. On average, 12 ticket holders cancel their reservations at the last minute, so the company intentionally overbooks the flight. Cancellations can be described by a normal distribution with a standard deviation of 4.8. Profit per passenger is $100. If a passenger arrives but cannot board due to overbooking, the company policy is to provide compensation of $91.
What is the optimal probability of having one or more empty seats on the plane?