An aircraft has 200 seats. The airline knows that, on average, 5% of the people who have purchased the ticket don’t show up. What is the maximum number of tickets they can sell to manage the probability that more than 200 passengers will show up at 10%?
The number of people who do not show up (X) will follow a binomial distribution with a probability of success of 5%, X ~ Bin(200+X, 0.05). Since X is unknown, we first use the qbinom function on 200 to get an approximate solution.
qbinom(0.1, 200, prob = 0.05, lower.tail = TRUE) 6Now, we use 200+6 in the equation.
qbinom(0.1, 206, prob = 0.05, lower.tail = TRUE)6
