Question

According to a flight statistics website, in 2009, a certain airline had the highest percentage of on-time flights in the airlines industry, which was 81.2%. Assume this percentage still holds true for that airline. Use the normal approximation to the binomial distribution to complete parts a through c below. b. Determine the probability that, of the next 30 flights from this airline, exactly 27 flights will arrive on time.

Answer #1

b)

n= | 30 | p= | 0.8120 |

here mean of distribution=μ=np= | 24.36 | |

and standard deviation σ=sqrt(np(1-p))= | 2.14 | |

for normal distribution z score =(X-μ)/σx |

therefore from normal approximation of binomial distribution and continuity correction: |

probability that, of the next 30 flights from this airline, exactly 27 flights will arrive on time :

probability
=P(26.5<X<27.5)=P((26.5-24.36)/2.14)<Z<(27.5-24.36)/2.14)=P(1<Z<1.47)=0.9292-0.8413=0.0879 |

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