For a Poisson distribution model, if the arrival rate of passengers at an airport is recorded as 30 per hour, the probability of exactly 4 arrivals in the first 10 minutes of an hour is:

Given:
$$\lambda = 30$$​ per hour
Time interval = 10 minute  = $$= \frac{1}{6}$$​ hour
​$$\Rightarrow \lambda' = 30 \times \frac{1}{6} = 5 \\k = 4 \\$$​​
Formula used:
​$$P(X = k) = \frac{\lambda'^k \cdot e^{-\lambda'}}{k!} \\$$​​
Solution:
​$$P(X = 4) = \frac{5^4 \cdot e^{-5}}{4!}$$​​
Correct answer is (b)