Final answer:
The Poisson probability of observing exactly 3 events when the average number of events is 5 is calculated using the Poisson distribution formula, giving a result of approximately 0.1404.
Step-by-step explanation:
To calculate the Poisson probability of getting exactly 3 events (calls) when the average number of events is 5, you use the formula for the Poisson probability distribution function:
P(X = x) = (e-λ * λx) / x!
Given λ = 5, and we want to find P(X = 3), we plug in the values:
P(X = 3) = (e-5 * 53) / 3!
This simplifies to:
P(X = 3) = (0.00674 * 125) / 6
P(X = 3) = 0.1404 (rounded to four decimal places)
Therefore, the probability of observing exactly 3 calls when the average number is 5 is approximately 0.1404.