Problem 3 An air flight regularly scheduled every weekday morning to Orlando can

Question

Problem 3 An air flight regularly scheduled every weekday morning to Orlando can hold 130 fare paying customers. A passenger with a reserved seat arrives on time for the flight with probability 0.95. Assume passengers behave independently What is the minimum number of seats the airline should reserve for the probability of a full flight to be at least 0.90? What is the maximum number of seats the airline should reserve so the number of on-time arrivals does not exceed the capacity with probability no more than 0.10? Given the probability of a reserved seat passenger arriving on time is 0.95, what is the mean and standard deviation of the number of such arrivals? If the airline follows a policy of taking standby names, and you decide you want to go to Disney World tomorrow but the flight is sold out, how do you feel about getting up early and going to the airport and getting on the standby list? What do you think about the assumptions that are required in order to use the binomial model in this problem? Hint: These can be pretty readily solved with either your TI calculator using the binomcdf function or easier with Minitab

Explanation / Answer

Number of fare paying customers = 130

Pr(a random passenger will arrive for the flight) = 0.95

(a) Here let say airlines reserved n number of seats and there are x number of seats are occupied.

Pr(X >= 130 ; n ; 0.95) >= 0.90

Pr(X < 130 ; n; 0.95) < 0.10

So by binomial cdf.

n would be 140 here.

(ii) SO, number of on time arrival doesn't exceeds the capacity with no more than 0.10. Lets n are the number of reservations done and number of arrivals are X.

Pr(X >130 ; n ; 0.95) < 0.10

Pr(X < = 130 ; n ; 0.95) > 0.90

so here n would be 134

(c) Mean of such arrivals = 130 * 0.95 = 123.5

Standard deviation of such arrivals = sqrt (130 * 0.05 * 0.95) = 2.485

(d) It would be very pathetic to know that i would be on standaby list of the airlines.

(e) Here each and every reservation must be indepenent of each other and all reservations must be random in nature.

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