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 166 passengers. If the airline believes the rate of passenger? no-shows is 6?% and sells 178 ?tickets, is it likely they will not have enough seats and someone will get? bumped? A)Use the normal model to approximate the binomial to determine the probability of at least 167 passengers showing up. B) Should the airline change the number of tickets they sell for this? flight? Explain.

Answer #1

P(Failure)= 0.06

P(Success)= 0.94

n= 178

A) Using binomial distribution:

n= 178, r= 167,168,169,170,171,172,173,174,175,176,177,178

p= 0.94 and (1-p)= 0.06

r | P® |

167 | 0.122622 |

168 | 0.125785 |

169 | 0.116605 |

170 | 0.096714 |

171 | 0.070886 |

172 | 0.045197 |

173 | 0.024558 |

174 | 0.011056 |

175 | 0.003959 |

176 | 0.001057 |

177 | 0.000187 |

178 | 1.65E-05 |

Yes, passers has to bumped.

B) The probability of at least 167 is higher than the failures of occurring. So, it has to change the number of tickets they sell for this.

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