Overbooking flights is a common practice of most airlines. A particular airline, believing that 3% of passengers fail to show for flights, overbooks (sells more tickets than there are seats). Suppose that for a particular flight involving a jumbo-jet with 267 seats, the airline sells 278 tickets. Question 1. What is the expected number of ticket holders that will fail to show for the flight

The expected number of ticket holders that will fail to show for the flight is 8.34.

Step-by-step explanation:

For each passenger, there are only two possible outcomes. Either they fail to show up to the flight, or they do not. The probability of a passenger not showing up is independent of other passengers. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

The expected value of the binomial distribution is:

3% of passengers fail to show for flights

This means that

The airline sells 278 tickets

This means that

What is the expected number of ticket holders that will fail to show for the flight

The expected number of ticket holders that will fail to show for the flight is 8.34.

arrange the equations with like terms in columns.

analyze the coefficients of x or y.

add the equations and solve for the remaining variable.

substitute the value into either equation and solve.

check the solution.

step-by-step explanation: