An airline knows that, on average,
the probability that a passenger will not show up for a flight is 6%.
If an airplane is fully booked and holds 300 passengers, how many
seats are expected to be empty? If the airline overbooked the flight by
10 passengers, about how many passengers are expected to show
up for the flight? Justify your answer
.06 * 300 = 18 empty (answer)
.06 * 310 = 18.6 do not show of the 310
310 - 18.6 = 291.4 show up (answer)
additionally
300 seats - 291.4 passengers = 8.6 empty seats which is really 18 empty because 40% of a passenger takes a whole seat
To find the number of seats expected to be empty, we need to calculate 6% of the total number of seats.
Step 1: Calculate 6% of 300.
6% of 300 = (6/100) * 300 = 0.06 * 300 = 18
Therefore, the airline expects approximately 18 seats to be empty.
To find the number of passengers expected to show up for the flight, we need to deduct the expected number of no-show passengers from the total number of passengers.
Step 1: Calculate the total number of passengers.
Total number of passengers = Number of seats - Overbooking
Total number of passengers = 300 - 10 = 290
Therefore, the airline expects approximately 290 passengers to show up for the flight.
To find out how many seats are expected to be empty, we need to calculate the probability that each individual passenger does not show up for the flight. Since we know that, on average, the probability of a passenger not showing up is 6%, we can calculate the expected number of empty seats using the following formula:
Expected number of empty seats = Total number of seats * Probability of a passenger not showing up
Given that there are 300 seats on the airplane, we can substitute these values into the formula:
Expected number of empty seats = 300 * 0.06 = 18
Therefore, we can expect about 18 seats to be empty.
Now, let's calculate the expected number of passengers who will show up for the flight, considering that the airline overbooked by 10 passengers. To find this, we need to subtract the expected number of empty seats from the total number of seats after overbooking:
Expected number of passengers to show up = Total number of seats - Expected number of empty seats
Total number of seats after overbooking = 300 + 10 = 310
Expected number of passengers to show up = 310 - 18 = 292
Therefore, we can expect about 292 passengers to show up for the flight.