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 81.3​%. Assume this percentage still holds true for that airline. Determine the probability​ that, of the next 30 flights from this​ airline, less than 23 flights will arrive on time

Answer 1

Using Normal approximation to Binomial

Mean = n * P = 30 * 0.813 = 24.39

Standard deviation =

P(X < 23 )

Using continuity correction

P ( X < 23 ) = P ( X < 23 - 0.5 ) = P ( X < 22.5 )

P ( X < 22.5 )
Standardizing the value

Z = ( 22.5 - 24.39 ) / 2.1356
Z = -0.88

P ( X < 22.5 ) = P ( Z < -0.88 )
P ( X < 22.5 ) = 0.1894

P ( X < 30 ) = 0.1894