a between and Town is unblocked? route Town A B Question 2 10 marks Two competin

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a between and Town is unblocked? route Town A B Question 2 10 marks Two competing airlines determine that a randomly chosen passenger who booked a seat on their airplanes fails to show with probability 20. To ensure their planes are always full, both airlines try to account for passengers not showing and overbook their flights to ensure every flight is full. Airline A has a 19 seat plane and always books 20 people, while Airline B has a 38 seat plane and always books for 40 people. Let A be the random number of passengers who show to board Airline A's plane and let B be the random number of people who show to board Airline B's plane. (a) With reasoning, determine the distribution of the random variables A and B, giving the correct PMF for each random variable. (b) For each airline, what is the probability that too many people show and hence, someone doesn't have a seat? ninimim (c) Using Airline A's current policy, what is thepanter probability someone fails to show for their seat (currently, this is 20.05) hich would ensure the probability that someone doesn't have a seat on Airline A's plane is less than 0.2? d) Airline A's policy is to always book one extra seat. For example, for a 15 seat plane they would book 16 people, or for a 30 seat plane, they would book 31. What size plane (how many seats) should Airline A use to ensure the probability someone doesn't have a seat is less than 0.1? on 3 10 marks

Explanation / Answer

Solution-

1. Both random variables A and B must follow binomial random variable.

A must follow binomial distibution with parameters - n = 20 and p = 1-1/20 = 0.95

B must follow binomial distibution with parameters - n = 40 and p = 1-1/20 = 0.95

2. P( too much people show in A) = P(A =20)

= 20c20 * 0.9520 * 0.050

= 0.3584

P( too much people show in B) = P(B=39) + P(B =40)

= 40c39 * 0.9539 * 0.051 + 40c40 * 0.9540 * 0.050

= 0.399

3. Let required probability be a. Then Required condition says-

. P( too much people show in A) = P(A =20) < 0.2

= 20c20 * (1-a)20 * a0 < 0.2

= 0.07732 - minimum probability.

4. Let required number of seats to be booked be n. Then, Required consition says-

P( too much people in A) = P(A=n) < 0.1

= ncn * 0.95n * 0.050 < 0.1

= n = 44

hence A should use 43 seat plane for the same

Answer

TY!

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