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