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Air-USA has a policy of booking as many as 22 people on an airplane that can only seat 20 people. (Past studies have revealed that only 82% of the booked passengers actually show up for the flight.) a) Find the probability that if Air-USA books 22 people, not enough seats will be available. Round your answer to 4 decimal places. P ( X > 20 )

Respuesta :

Answer:

The answer is "0.07404893".

Step-by-step explanation:

Applying the binomial distribution:

[tex]n = 22\\\\p= 82\%=0.82\\\\q = 1-0.82 = 0.18\\\\[/tex]

Calculating the probability for not enough seats:

[tex]=P(X>20)\\\\= P(21) + P(22)\\\\[/tex]

[tex]= \binom{22}{21} (0.82)^{21}(0.18)^1+ \binom{22}{22} (0.82)^{22}(0.18)[/tex]

[tex]=0 .06134598+ 0.01270295\\\\=0.07404893[/tex]

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