To calculate the Poisson probability $P(X = 9)$ with $\lambda = 14$, we use the Poisson probability formula:

$P(X = k) = \frac{e^{-\lambda} \cdot \lambda^k}{k!}$

Here:

• $\lambda = 14$
• $k = 9$
• $e \approx 2.71828$

Now let's compute the probability.The Poisson probability $P(X = 9)$ for $\lambda = 14$ is approximately 0.0473.

Would you like more details on this calculation or have any further questions?

Here are five related questions to consider:

1. How does the Poisson distribution change when $\lambda$ increases?
2. What is the cumulative probability $P(X \leq 9)$ for the same $\lambda = 14$?
3. How do you interpret the result of $P(X = 9)$ in a real-world scenario?
4. How does the Poisson distribution compare to the binomial distribution for large $\lambda$?
5. How do you compute the mean and variance of a Poisson distribution?

Tip: The mean and variance of a Poisson distribution are both equal to $\lambda$.