Question

The U.S. divorce rate has been reported as 4.2 divorces per 1000 population. Assuming that this rate applies to a small community of just 200 people and is Poisson distributed, what is the probability that exactly two divorces will occur in this community?

Answer 1

To find the probability of exactly 2 divorces occurring in a small community with a divorce rate of 4.2 per 1000 population, we can use the Poisson distribution formula. Plugging in the values, the probability is approximately 0.2002.

Step-by-step explanation:

To solve this problem, we can use the Poisson distribution formula:

P(x; λ) = (e^(-λ) * λ^x) / x!

Where:

• P(x; λ) is the probability of getting x divorces in a community
• λ is the average number of divorces per 1000 population, which is 4.2/1000 * 200 = 0.84
• x is the number of divorces we want to find the probability for, which is 2

Plugging these values into the formula, we get:

P(2; 0.84) = (e^(-0.84) * 0.84^2) / 2!

P(2; 0.84) ≈ 0.2002

Therefore, the probability that exactly two divorces will occur in this community is approximately 0.2002.