Sixty-four percent of all airplanes arriving at an airport are late. Using the binomial formula, what is the probability that in a random sample of seven airplanes, exactly four will arrive late?

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Answer 1 · 2016-12-27T05:48:11

0.274

Binomial Theoram,
#P(X=k) = ("_k^n)*p^(n)*q^(n-k)#

#n=7, k=4, p=0.64, q=0.36#

#P(X=4) = ("_4^ 7)*0.64^4*0.36^3#

#P(X=4) = (7!)/(4!*3!) *0.64^4*0.36^3#

#P(X=4) = (7*cancel 6*5*cancel(4*3*2*1)/(cancel(4*3*2*1)*cancel(3*2)*1)*0.64^4*0.36^3)#

#P(X=4) = 35*0.64^4*0.36^3#

#P(X=4) = 0.274# (3 dec points)