An airline charges the following baggage fees: $30 for the first bag and $35 for the second. Suppose 51% of passengers have no checked luggage, 27% have only one piece of checked luggage and 22% have two pieces. We suppose a negligible portion of people check more than two bags.
sounds reasonable.
So, what? Something tells me you want something involving
0.51(0) + 0.27(30) + 0.22(35)
which would be the cost for all the expected checked bags
To find the average baggage fee per passenger, we need to calculate the weighted average of the baggage fees based on the percentages given.
Let's break down the calculation step by step:
1. Calculate the total number of passengers who checked luggage:
- From the given percentages, we know that 51% have no checked luggage and 27% have only one piece of checked luggage.
- Therefore, the percentage of passengers who checked luggage is 100% - 51% - 27% = 22%.
2. Calculate the average number of bags per passenger:
- Since only 22% of passengers have two pieces of checked luggage, the average number of bags per passenger would be less than 2.
- Let's calculate it:
- The percentage of passengers with no checked luggage (51%) accounts for 0 bags per passenger.
- The percentage of passengers with one piece of checked luggage (27%) accounts for 1 bag per passenger.
- The percentage of passengers with two pieces of checked luggage (22%) accounts for 2 bags per passenger.
- Multiply the bag count by the respective percentage and add them together: (0 x 51%) + (1 x 27%) + (2 x 22%) = 0 + 0.27 + 0.44 = 0.71 bags per passenger.
3. Calculate the average baggage fee per bag:
- The first bag costs $30, and the second bag costs $35.
- The average cost per bag is the weighted average of these two costs, where the weights are the percentage of passengers with 1 or 2 pieces of checked luggage.
- Calculate the average as follows: ($30 x 27% + $35 x 22%) / 0.71 = ($8.1 + $7.7) / 0.71 = $16.8 / 0.71 ≈ $23.66.
Therefore, the average baggage fee per passenger is approximately $23.66.