B.) using the binomial distribution, what is the probability that in the next si

Question

B.) using the binomial distribution, what is the probability that in the next six flights all six will be on time? C.) using the binomial distribution, What is the probability that in the next six flights at least four flights will be in time? ore: 0 of 1 pt 3.22 govemments department of transportation reported that in 2009, airline A led all domestic airlines in on-time arrivals for domestic flights, with a rate of 0.826 Complete parts (a) through (e) below Using the binomial distribution, what is the probability that in the next six fights, four fights will be on time? he probability is 5 of 10 (8 complete) Hw Score: 58.89% Round to four decimal plaoes as needed.) places as needed.)

Explanation / Answer

X ~ Binomial (n,p)

Where n = 6, p = 0.826

Binomial probability distribution is

P(X) = nCx px (1-p)n-x

a)

P( X = 4) = 6C4 0.8264 0.1742

= 0.2114

b)

P( X = 6) = 6C6 0.8266 0.1740

= 0.3176

c)

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

= 6C4 0.8264 0.1742 + 6C5 0.8265 0.174 + 6C6 0.8266 0.1740

= 0.9304

d)

Mean = n * p

= 6 * 0.826

= 4.956

Standard deviation = Sqrt( n p( 1 -p) )

= sqrt( 6 * 0.826 * 0.174)

= 0.928625

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