Final answer:
To find the probability that there is not enough seats for an Air-USA flight, we can use the binomial distribution formula. By calculating the probability of more than 20 passengers arriving, we find that the probability of not enough seats is approximately 99.97%.
Step-by-step explanation:
To find the probability that there is not enough seats for an Air-USA flight, we need to consider two factors: the number of booked passengers and the actual number of passengers that arrive for the flight.
Given that Air-USA has a policy of booking as many as 22 persons on an airplane that can seat only 20, we can calculate the probability of more than 20 passengers arriving for the flight using the binomial distribution formula.
The probability of more than 20 passengers arriving can be calculated as follows:
P(X > 20) = 1 - P(X ≤ 20)
Where X follows a binomial distribution with n = 22 and p = 0.89 (probability of a passenger arriving).
Using a calculator or statistical software, we can find that P(X ≤ 20) = 0.0003002274.
Therefore, the probability of not enough seats for an Air-USA flight is:
P(X > 20) = 1 - P(X ≤ 20) = 1 - 0.0003002274 = 0.9996997726 or approximately 99.97%.