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Suppose p is the number of cars per minute passing through a certain road junction between 5 PM and 6 PM, and p has a Poisson distribution with mean 3. What is the probability of observing fewer than 3 cars during any given minute in this interval?

1. 8/(2e³)
2. 9/(2e³)
3. 17/(2e³)
4. 26/(2e³)

Correct answer: 17/(2e³)

Solution

The probability of observing fewer than 3 cars in a Poisson distribution can be calculated by summing the probabilities of observing 0, 1, and 2 cars. Given the mean of 3, the calculations yield a total probability of 17/(2e³) for these events.

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