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.
|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 :
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