A governments department of transportation reported that in

A governments department of transportation reported that in 2009 airline a led to all domestic airline on time arrivals for domestic flights, with a rate of 0.843. What is the probability that of the next 6 flights 4 will be on time? all 6 of 6 flights on time? Atleast 4 on time of the next six flights? What are the mean and standard deviation of the number of on time arrivals? Round to 4 decimal places please.

Solution

What is the probability that of the next 6 flights 4 will be on time?

Given X follows Binomial distribution with n=6 and p=0.843

P(X=x)=6Cx*(0.843^x)*((1-0.843)^(6-x)) for x=0,1,2,..,6

So P(X=4) =6C4*(0.843^4)*((1-0.843)^(6-4)) =0.1867243

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all 6 of 6 flights on time?

P(X=6) =6C6*(0.843^6)*((1-0.843)^(6-6)) =0.3588934

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Atleast 4 on time of the next six flights?

P(X>=4) = P(X=4)+P(X=5)+P(X=6) =0.9466587

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What are the mean and standard deviation of the number of on time arrivals?

mean= n*p=6*0.843 = 5.058

standard deviation =sqrt(n*p*(1-p))

=sqrt(6*0.843*(1-0.843))

=0.8911263