3) Airlines sometimes overbook flights. Suppose that for a plane with 100 seats, an airline takes 110
reservations. Define the variable x as the number of people who actually show up for a sold-out
flight. From past experience, the population distribution of x is given in the following table:
a. What is the probability that the airline can accommodate everyone who shows up for the flight?
b. What is the probability that not all passengers can be accommodated?
c. If you are trying to get a seat on such a flight and you are number 1 on the standby list, what is the
probability that you will be able to take the flight? What if you are number 3?
Answers
Given :- Airlines sometimes overbook flights. Suppose that for a plane with 100 seats, an airline takes 110 reservations. Define the variable x as the number of people who actually show up for a sold-out flight. From past experience, the population distribution of x is given in the following table .
a. What is the probability that the airline can accommodate everyone who shows up for the flight ?
Answer :-
given that, the airline has 100 seats . so, the airline can accommodate maximum 100 passengers .
then,
→ P(x ≤ 100) = p(95) + p(96) + p(97) + p(98) + p(99) + p(100)
putting values from table we get,
→ P(x ≤ 100) = 0.05 + 0.10 + 0.12 + 0.14 + 0.24 + 0.17
→ P(x ≤ 100) = 0.82 (Ans.)
b. What is the probability that not all passengers can be accommodated ?
Answer :-
since there are only 100 seats, the airline cant accommodate the passengers whose reservation is after 100 .
so,
→ P(x > 100) = p(101) + p(102) + p(103) + p(104) + p(105) + p(106) + p(107) + p(108) + p(109) + p(110)
again putting given proportion values from table we get,
→ P(x > 100) = 0.06 + 0.04 + 0.03 + 0.02 + 0.01 + 0.005 + 0.005 + 0.005 + 0.0037 + 0.0013
→ P(x > 100) = 0.18 (Ans.)
c. If you are trying to get a seat on such a flight and you are number 1 on the standby list, what is the probability that you will be able to take the flight ? What if you are number 3 ?
Answer :-
If i m number 1 on the standby list maximum 99 passengers can take the flight .
so,
→ p(x ≤ 99) = p(95) + p(96) + p(97) + p(98) + (99)
→ p(x ≤ 99) = 0.05 + 0.10 + 0.12 + 0.14 + 0.24
→ p(x ≤ 99) = 0.65 (Ans.)
and if i am at number 3,
→ p(x ≤ 97) = p(95) + p(96) + p(97)
→ p(x ≤ 97) = 0.05 + 0.10 + 0.12
→ p(x ≤ 97) = 0.27 (Ans.)
Learn more :-
7cm long stick cut in three pieces. Length of each piece is natural number.
What is the probability of forming triangl...
https://brainly.in/question/37342919
Ang, Ben, and Jasmin each have 5 blocks, colored red, blue, yellow, white, and green; and there are 5 empty boxes. Each ...
https://brainly.in/question/34973202
If a die is rolled twice, what is the probability that the sum of the points is more than 9
https://brainly.in/question/8806537