Question

2.38 Baggage fees: An airline charges the following baggage fees: $25 for the first bag and an extra $35 for the second. Suppose 54% of passengers have no checked luggage, 34% have only one piece of checked luggage and 12% 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

2.36 Is it worth it?: Andy is always looking for ways to make money fast. Lately, he has been trying to make money by gambling. Here is the game he is considering playing: The game costs $2 to play. He draws a card from a deck. If he gets a number card (2-10), he wins nothing. For any face card ( jack, queen or king), he wins $3. For any ace, he wins $5, and he wins an extra $20 if he draws the ace of clubs. Round answers to 2 decimal places.

a) Andy's expected profit per game is: $  


b) Would you recommend this game to Andy as a good way to make money? Explain.

• No, we expect Andy to lose money each time he plays this game
• Yes, Andy could be lucky and might earn money in the long-run playing this game

Consider the discrete random variable XX given in the table below. Calculate the mean, variance, and standard deviation of XX.

XX	2	3	6	17	19	20
P(XX)	0.08	0.12	0.46	0.12	0.14	0.08

μμ =
σ2σ2 =
σσ =

What is the expected value of XX?

A probability distribution of the claim sizes for an auto insurance policy appears in the following table.

Claims	Probability
1	0.1
2	0.2
3	0.1
4	0.25
5	0.35

Find the percentage of claims within one standard deviation of the mean.     %

Answer 1