619 According to FlightStatscom in 2009 Southwest Airlines h

6.19 According to FlightStats.com, in 2009, Southwest Airlines had the highest percentage of on-time flights in the airlines industry, which was 82.5%. Assume this percentage still holds true for Southwest Airlines. Using the normal approximation to the binomial distribution, determine the probability that, of the next 30 Southwest Airlines flights,

a) less than 22 flights will arrive on time

b) exactly 26 flights will arrive on time

c) 21,22,23,or 24 will arrive on time

d) 24,25,26,27, or 28 flights will arrive on time

Solution

a) less than 22 flights will arrive on time

Given X follows Binomial distribution with n=30 and p=0.825

P(X=x)=30Cx*(0.825^x)*((1-0.825)^(30-x)) for x=0,1,2,..,30

So P(X<22) = P(X=0)+P(X=1)+...+P(X=21)

=30C0*(0.825^0)*((1-0.825)^(30-0))+...+30C21*(0.825^21)*((1-0.825)^(30-21))

=0.06580159

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b) exactly 26 flights will arrive on time

P(X=26) = 30C26*(0.825^26)*((1-0.825)^(30-26)) =0.1728959

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c) 21,22,23,or 24 will arrive on time

P(21<=X<=24) = P(X=21)+P(X=22)+P(X=23)+P(X=24) =0.4046658

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d) 24,25,26,27, or 28 flights will arrive on time

P(24<=X<=28) = P(X=24)+...+P(X=28) =0.7139067