Because many passengers who make reservations do not show up, airlines often ove
ID: 3359575 • Letter: B
Question
Because many passengers who make reservations do not show up, airlines often overbook flights (sell more tickets than there are seats). A certain airplane holds 286 passengers. If the airline believes the rate of passenger no-shows is 9% and sells 312 tickets, is it likely they will not have enough seats and someone will get bumped? Bold a right parenthesis font size decreased by 1 a) Use the normal model to approximate the binomial to determine the probability of at least 287 passengers showing up. Bold b right parenthesis font size decreased by 1 b) Should the airline change the number of tickets they sell for this flight? . The probability of at least 287 passengers showing up ?(Round to three decimal places as needed
Explanation / Answer
Ans:
Binomial distribution with n=312,probability of show up,p=1-0.09=0.91
P(bumped)=P(x>286)=1-P(x<=286)=1-BINOMDIST(286,312,0.91,TRUE)=1-0.6879=0.3121
As,probability of showing up more than 286 is very large 0.3121,it is likely that not have enough seats and someone will get bumped
a)Normal approximation
mean=np=312*0.91=283.92
standard dev=sqrt(312*0.91*0.09)=5.055
z=(287-283.92)/5.055=0.61
P(z>=0.61)=1-P(z<0.61)=1-0.7291=0.2709
b)Yes,as probability of showing up atleast 287 passengers is fairly high,they should change the number of tickets,they sell for this flight.