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

5

The correct answer is Option (2) → 5

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. 

$∴ E(X) = 30 ×\frac{1}{6} =5$

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