Problem 3: Discrete probability distribution& mean&SD; An airline charges follow

Question

Problem 3: Discrete probability distribution& mean&SD; An airline charges following baggage fees. S25 for the first bag and S35 for the second Suppose 54% of passengers have no checked luggage, 34% have one piece of checked luggage and 1,2% have two pieces. We suppose a negligible portion of people check more than two bags. the (1) Build a probability model, compute the average revenue per passenger, and compute the corresponding standard deviation. (10 pts) (2) About how much revenue should the airline expect for a flight of 120 passengers? (3 pts) With what standard deviation? (3 pts) 20 X

Explanation / Answer

1) from above probability of 0 revenue =P(X=0) =probability of no luggage =0.54

P(X=25)= probability of one luggage =0.34

P(X=25+35=60)=probability of two bag luggage=0.12

therefore from above:

average revenue per pessanger =$15.70

std deviation =$19.95

2)expected revenue for 120 customers =120*15.70=1884

std deviation =19.95*(120)1/2 =$218.54

please revert for any clarificaiton

x p(x) xP(x) x2P(X) (x-)2 (x-)2P(x) 0 0.5400 0.000 0.000 246.490 133.105 25 0.3400 8.500 212.500 86.490 29.407 60 0.1200 7.200 432.000 1962.490 235.499 total 1 = 15.70 644.500 2295.470 2= 398.0100 std deviation=     =    2 = 19.9502

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