Mean and Distribution of Vehicular Arrival Rate
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The given problem states that the vehicular arrival at an isolated intersection follows the Poisson distribution with a mean arrival rate of 2 vehicles per minute.

- The Poisson distribution is commonly used to model the number of events occurring in a fixed interval of time or space.
- In this case, the mean arrival rate of 2 vehicles per minute tells us that, on average, 2 vehicles arrive at the intersection every minute.

Probability of at least 2 vehicles arriving in a 1-minute interval
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We need to find the probability that at least 2 vehicles will arrive in any given 1-minute interval.

- Let's denote this probability as P(X >= 2), where X represents the number of vehicles arriving in the 1-minute interval.
- To find this probability, we can use the cumulative distribution function (CDF) of the Poisson distribution.

Using Cumulative Distribution Function
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The CDF of the Poisson distribution gives the probability that the number of events is less than or equal to a certain value.

- In this case, we want to find the probability that the number of vehicles is greater than or equal to 2, which is the complement of the probability that the number of vehicles is less than 2.
- Mathematically, we can express this as P(X >= 2) = 1 - P(X < />

Calculating the Probability
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To calculate the probability P(X < 2),="" we="" can="" use="" the="" poisson="" probability="" mass="" function="" />

- The PMF of the Poisson distribution is given by P(x) = (e^(-λ) * λ^x) / x!, where λ is the mean arrival rate and x is the number of events.
- We can calculate P(X < 2)="" as="" p(x="0)" +="" p(x="" />

Calculating P(X = 0)
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P(X = 0) = (e^(-2) * 2^0) / 0! = e^(-2) ≈ 0.1353

Calculating P(X = 1)
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P(X = 1) = (e^(-2) * 2^1) / 1! = 2e^(-2) ≈ 0.2707

Calculating P(X < />
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P(X < 2)="P(X" =="" 0)="" +="" p(x="1)" ≈="" 0.1353="" +="" 0.2707="" ≈="" />

Calculating P(X >= 2)
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P(X >= 2) = 1 - P(X < 2)="" ≈="" 1="" -="" 0.4060="" />

Therefore, the probability that at least 2 vehicles will arrive in any given 1-minute interval is approximately 0.59, rounded off to 2 decimal places.