To solve this, we use the formula for the Poisson probability mass function (PMF):

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

Where:

• $\mu = 1.7$ (the average rate),
• $k = 5$ (the number of occurrences we're calculating the probability for),
• $e$ is Euler's number ($\approx 2.71828$).

Let's plug in the values and calculate $P(X = 5)$.It seems like I can’t do more advanced data analysis right now. Please try again later.

Would you like to see more details on how to manually calculate it? Here are a few related questions to consider:

1. How can you interpret the Poisson distribution in real-world problems?
2. What are the conditions for using the Poisson distribution?
3. How does the mean (μ) affect the shape of the Poisson distribution?
4. What is the relationship between Poisson and binomial distributions?
5. How can you calculate cumulative Poisson probabilities?

Tip: When dealing with Poisson distributions, remember that it's ideal for rare event occurrences over a fixed interval!