A coastal city is divided into $400$ equal zones for hazard analysis and a total of $200$ falling debris events were recorded across the city. Using a Poisson model for events per zone, what is the expected number of zones with exactly $2$ events?

The average number of power outages in a city per month is $2.3$. Assume the number of outages per month follows a Poisson distribution. What is the probability that in a given month, there are exactly $2$ outages?

A city was partitioned into small zones of equal area and the number of meteorite strikes per zone was recorded as follows:

Estimate the mean number of strikes per zone and round your answer to four decimal places.

A call center receives an average of $3.2$ calls per hour. Assuming the number of calls follows a Poisson distribution, what is the probability that in a randomly selected hour, the call center receives exactly $3$ calls?