Airline passenger arrive randomly and independently at the

Answered question

2022-02-05

Airline passenger arrive randomly and independently at the passenger screening facility at a major international airport with mean arrival rate of 10 passenger per minute. 1. what is the probability that exactly 7 passengers arrive in a minute period? 2.what is the probability that at the most 5 passengers would in a minute period? 3.what is the probability that number of passenger in a minute would be between 8 and 12 both inclusive?

Answer & Explanation

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Skilled2023-04-22Added 403 answers

Given information: Mean arrival rate of passengers at a major international airport is 10 passengers per minute.

Let's assume that the passenger arrival follows a Poisson distribution with parameter λ=10, which gives the probability of the number of passengers arriving in a minute period.

1. The probability of exactly 7 passengers arriving in a minute can be calculated using the Poisson distribution as follows:

P(X=7)=λxe-λx!
         =107e-107!
         =0.0908 (rounded to four decimal places)

Therefore, the probability of exactly 7 passengers arriving in a minute is 0.0908.

2. The probability of at most 5 passengers arriving in a minute can be calculated by summing up the probabilities of having 0, 1, 2, 3, 4, or 5 passengers arriving in a minute. This can be written mathematically as:

P(X5)=Σλxe-λx!, where x = 0 to 5

         =[100e-100!]+[101e-101!]
           +[102e-102!]+[103e-103!]
           +[104e-104!]+[105e-105!]

         =0.0671(rounded to four decimal places)

Therefore, the probability of at most 5 passengers arriving in a minute is 0.0671.

3. The probability of having between 8 and 12 passengers arriving in a minute, both inclusive, can be calculated by summing up the probabilities of having 8, 9, 10, 11, or 12 passengers arriving in a minute. This can be written mathematically as:

P(8X12)=λxe-λx!, where x = 8 to 12

                =[108e-108!]+[109e-109!]
                  +[1010e-1010!]+[1011e-1011!]
                  +[1012e-1012!]

                =0.3213 (rounded to four decimal places)

Therefore, the probability of having between 8 and 12 passengers arriving in a minute, both inclusive, is 0.3213.

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