Question

# According to a flight statistics​ website, in​ 2009, a certain airline had the highest percentage of​...

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.

b)

 n= 30 p= 0.812
 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

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