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What makes this a Poisson distribution(3 conditions) and what is the probability?

What makes this a Poisson distribution(3 conditions) and what is the probability?-example-1

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Answer:

Probability = 0.2865

Explanation:

There are 65 accidents per year. We know that there are 52 weeks in a year, so let us determine the number of accidents in a week.

65/52 = 1.25 accidents in a week

If we use Poisson distribution, remember that X = the number of occurrences of a particular event in an interval of time or space. In this case X = 0, as we need to find the probability of there being no accidents. Our set up...

P(X = x) = λ^x * e^-λ / x!,

1 week => λ = 1.25,

P(X = 0) = 1.25^0 * e^-1.25/0!

= 1 * e^-1.25

= 1/e^1.25 ≈ 0.2865

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