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

0.174

The correct answer is Option (3) → 0.174

Given number of arrivals per hour is 30.

Let the random variable X be the number of arrivals in first 10 minutes of an hour i.e. $\frac{1}{6}$ hour. 

$∴ E(X) = 30 ×\frac{1}{6} =5$

the expected number of arrivals in the first 10 minutes of an hour is 5.

For first 10 minutes of an hour $λ = 5$.

∴ P(exactly 4 arrivals in first 10 minutes of an hour)

$=\frac{5^4e^{-5}}{4}=\frac{625 × 0.0067}{24}= 0.174$