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?
Your assumption that there is no relationship between those who carry the luggage and those who do not carry the luggage is reasonable in this context. It is stated that a negligible portion of people check more than two bags and there is no mention of any correlation between passengers with and without luggage. Therefore, you can assume that these two groups are independent.
Another assumption you can make is that the percentage distribution of passengers with no checked luggage, one piece of checked luggage, and two pieces of checked luggage remains the same for a flight of 120 passengers. In other words, you can assume that the proportions of passengers in each category are still 54%, 34%, and 12% respectively. This assumption is reasonable unless there are specific factors that would cause a significant change in the distribution of luggage carrying passengers.
Your E(x) = $12.70 is correct
your $1524 is correct
I am not familiar with 'standard deviation' in this context