An airline charges the following baggage fees: $25 for the first 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.
(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.

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empathictruro empathictruro · Answer 1 · 2020-01-26T09:54:06+01:00

Answer:

The average revenue per passenger = E(x) = $15.70

[tex]\sigma = \sqrt{\sigma^{2}} = \sqrt{398} \approx 19.95[/tex]

b)$1,884 ± $20

Step-by-step explanation:

a)

Refer attached fig for probability model,

i)The average revenue per passenger = E(x) = $15.70

[tex]\sigma^{2} = V[X] \sum _{x} (x-\mu )^{2} \times P(X=x)[/tex]

[tex]\sigma^{2} = (0-15.7)^{2} \times 0.54+(25-15.7)^{2} \times 0.34 +(60-15.7)^{2} \times 0.12[/tex]

[tex]\sigma^{2} = 133.1 + 29.4 + 235.5 = 398[/tex]

Standard Deviation = [tex]\sigma = \sqrt{\sigma^{2}} = \sqrt{398} \approx 19.95[/tex]

ii) average revenue per passenger = E(x) = $15.70

b) Revenue should the airline expect for a flight of 120 passengers

revenue = 120 * $15.70 = $1,884 ± $20 (or 19.95 rounded up)

use same σ