2.38 Baggage fees: An airline charges the following baggage fees: for the ofirst bag and for the
second. Suppose of passengers have no checked luggage, have only one piece of checked luggage
and have two pieces. We suppose a negligible portion of people check more than two bags.
a) The average baggage-related revenue per passenger is: (please round to the
nearest cent)
b) The standard deviation of baggage-related revenue is: (please round to the
nearest cent)
c) About how much revenue should the airline expect for a flight of 120 passengers? $
(please round to the nearest dollar)

Ask by Marshall Schmidt. in the United States

Dec 07,2024

Question

2.38 Baggage fees: An airline charges the following baggage fees: for the ofirst bag and for the
second. Suppose of passengers have no checked luggage, have only one piece of checked luggage
and have two pieces. We suppose a negligible portion of people check more than two bags.
a) The average baggage-related revenue per passenger is: (please round to the
nearest cent)
b) The standard deviation of baggage-related revenue is: (please round to the
nearest cent)
c) About how much revenue should the airline expect for a flight of 120 passengers? $
(please round to the nearest dollar)

Ask by Marshall Schmidt. in the United States

Dec 07,2024

UpStudy AI · Accepted Answer

To solve the problem, we will first calculate the average baggage-related revenue per passenger and then the standard deviation of that revenue. Finally, we will estimate the expected revenue for a flight of 120 passengers.

### a) Average Baggage-Related Revenue per Passenger

Let:
- $$ P_0 = 0.54 $$ (probability of no checked luggage)
- $$ P_1 = 0.34 $$ (probability of one checked bag)
- $$ P_2 = 0.12 $$ (probability of two checked bags)

The revenue for each case is:
- No checked luggage: $$ R_0 = 0 $$
- One checked bag: $$ R_1 = 25 $$
- Two checked bags: $$ R_2 = 25 + 35 = 60 $$

Now, we can calculate the expected revenue $$ E(R) $$:

$$
E(R) = P_0 \cdot R_0 + P_1 \cdot R_1 + P_2 \cdot R_2
$$

Substituting the values:

$$
E(R) = 0.54 \cdot 0 + 0.34 \cdot 25 + 0.12 \cdot 60
$$

Calculating each term:

$$
E(R) = 0 + 8.5 + 7.2 = 15.7
$$

Thus, the average baggage-related revenue per passenger is:

$$
\boxed{15.70}
$$

### b) Standard Deviation of Baggage-Related Revenue

To find the standard deviation, we first need to calculate the variance. The variance $$ Var(R) $$ is given by:

$$
Var(R) = E(R^2) - (E(R))^2
$$

First, we calculate $$ E(R^2) $$:

$$
E(R^2) = P_0 \cdot R_0^2 + P_1 \cdot R_1^2 + P_2 \cdot R_2^2
$$

Calculating $$ R^2 $$ for each case:

- $$ R_0^2 = 0^2 = 0 $$
- $$ R_1^2 = 25^2 = 625 $$
- $$ R_2^2 = 60^2 = 3600 $$

Now substituting into $$ E(R^2) $$:

$$
E(R^2) = 0.54 \cdot 0 + 0.34 \cdot 625 + 0.12 \cdot 3600
$$

Calculating each term:

$$
E(R^2) = 0 + 212.5 + 432 = 644.5
$$

Now we can calculate the variance:

$$
Var(R) = E(R^2) - (E(R))^2 = 644.5 - (15.7)^2
$$

Calculating $$ (15.7)^2 $$:

$$
(15.7)^2 = 246.49
$$

Now substituting back into the variance formula:

$$
Var(R) = 644.5 - 246.49 = 398.01
$$

Now, the standard deviation $$ \sigma $$ is:

$$
\sigma = \sqrt{Var(R)} = \sqrt{398.01} \approx 19.95
$$

Thus, the standard deviation of baggage-related revenue is:

$$
\boxed{19.95}
$$

### c) Expected Revenue for a Flight of 120 Passengers

To find the expected revenue for a flight of 120 passengers, we multiply the average revenue per passenger by the number of passengers:

$$
\text{Expected Revenue} = E(R) \cdot \text{Number of Passengers} = 15.7 \cdot 120
$$

Calculating this:

$$
\text{Expected Revenue} = 1884
$$

Thus, the expected revenue for a flight of 120 passengers is:

$$
\boxed{1884}
$$
a) The average baggage-related revenue per passenger is $15.70. b) The standard deviation of baggage-related revenue is $19.95. c) The airline should expect $1884 for a flight of 120 passengers.

Upstudy AI Solution

Answer

Solution

c) Expected Revenue for a Flight of 120 Passengers

Mind Expander

c) Expected Revenue for 120 Passengers

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