Final answer:
The probability that the airline overbooked this flight is approximately 0.996 or 99.6%.
Step-by-step explanation:
To calculate the probability that the airline overbooked the flight, we need to determine the probability of more customers showing up than there are seats available. In this case, 310 tickets were sold for a flight with 298 seats. The percentage of no-shows is 3%, which means the probability of a customer not showing up is 0.03.
We can use the binomial probability formula to calculate the probability. Let X be the number of customers showing up:
P(X > 298) = 1 - P(X <= 298)
P(X <= 298) = (1 - 0.03)^310
≈ 0.004
P(X > 298) = 1 - 0.004
≈ 0.996
Therefore, the probability that the airline overbooked this flight is approximately 0.996 or 99.6%.