Baggage fees. An airline charges the following baggage fees: $25 for the rst bag and $35 for the second. Suppose 54% of passengers have no checked luggage, 34% have one piece of checked luggage and 12% have two pieces. We suppose a negligible portion of people check more than two bags.
(a) Build a probability model, compute the average revenue per passenger, and compute the corresponding standard deviation.
My answer:
Average revenue per passenger = E(X)= 12.70
Standard deviation= 14.08
(b) About how much revenue should the airline expect for a flight of 120 passengers? With what standard deviation? Note any assumptions you make and if you think they are justified.
My answer:
$12.70(120)= $1524
Standard deviation = 14.08 (the same)
I would assume that those not carrying the luggage do not have someone else's carrying it for them.. That is, there is no relationship between those who carry the luggage and those who do not carry the luggage.
Does my assumption make sense?
What other assumptions can I make?
Thank you!
Well, it seems like you're checking in some baggage fees, but let's not carry too much weight on our assumptions! Your assumption about there being no relationship between those who carry luggage and those who do not carry luggage seems reasonable given the information provided.
As for other assumptions, we could assume that the distribution of passengers and their luggage remains consistent across flights. We could also assume that the fees for each bag remain constant and do not change based on factors such as peak travel seasons or special promotions. Additionally, we could assume that the percentage of passengers with no, one, or two bags remains the same.
Overall, while assumptions can help us make calculations and predictions, it's important to acknowledge their limitations and keep a flexible mindset. After all, just like a checked bag, assumptions can sometimes get lost along the way!
Your assumption that there is no relationship between those who carry luggage and those who do not carry luggage is reasonable in this context. It is common to assume independence between different events or variables unless there is evidence to suggest otherwise.
Some other assumptions you can make in this scenario are:
1. Each passenger's baggage count is independent of others. This means that the probability distribution of the number of bags a passenger checks does not depend on the number of bags checked by other passengers.
2. The percentages given (54%, 34%, and 12%) accurately represent the entire population of passengers. This assumption implies that the sample provided is representative of the larger population, and there is no significant bias or selection issues.
3. The fees for baggage are fixed and do not vary based on any additional factors like weight or size of the bags. If the fees were variable, that would need to be considered in the calculation.
4. There are no outliers or extreme cases that significantly impact the average revenue calculation. In this case, it is assumed that each category of passengers (0 bags, 1 bag, 2 bags) contributes proportionally to the revenue.
By making these assumptions, you can confidently calculate the average revenue per passenger and the standard deviation for a flight of 120 passengers.
Your assumption that there is no relationship between those who carry the luggage and those who do not carry the luggage is reasonable. It is common practice to make this assumption when analyzing probabilities and expected values.
As for other assumptions, since the problem statement mentions a negligible portion of people checking more than two bags, we can assume that the number of bags checked follows a binomial distribution with parameters n = 2 and p = 0.34 (probability of checking one bag). Additionally, we can assume that each passenger is independent of each other when it comes to the number of bags checked.
These assumptions allow us to model the problem using a probability distribution and calculate the expected revenue and standard deviation accordingly.