Welcome to the article An airline company is considering a new policy of booking as many as 313 persons on an airplane that can seat only 290 Past studies. On this page, you will learn the essential and logical steps to better understand the topic being discussed. We hope the information provided helps you gain valuable insights and is easy to follow. Let’s begin the discussion!
Answer :
The probability that if the airline company books 313 persons, not enough seats will be available can be estimated using the binomial distribution. Given that only 87% of booked passengers actually arrive for the flight, the estimated probability is approximately 0.0161.
To estimate the probability, we can use the binomial distribution formula. Let's define the event of interest as "not enough seats available" and consider it a success. The probability of success is 1 - 0.87 = 0.13, which represents the probability that a booked passenger does not arrive for the flight.
The number of trials is 313, representing the number of persons booked by the airline company. We want to find the probability of having more than 290 successes, indicating that there are more passengers than available seats.
Using the binomial distribution formula, we can calculate the probability as follows:
[tex]P(X > 290) = 1 - P(X $\le$ 290) = 1 - \Sigma(k=0\ to \ 290) (313 \ choose \ k) * (0.13)^k * (1 - 0.13)^{(313 - k)}[/tex]
Since calculating the sum manually is tedious, we can use software or calculators to find the probability. The estimated probability that not enough seats will be available when booking 313 persons is approximately 0.0161.
Therefore, the probability, estimated using the binomial distribution, is approximately 0.0161 that if the airline company books 313 persons, not enough seats will be available.
Learn more about binomial distribution here:
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Rewritten by : Brahmana