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?

Which statement best defines the Poisson distribution and its parameter lambda?

You observe counts of a rare event over ten consecutive one-hour intervals resulting in counts: 1, 3, 2, 0, 4, 1, 2, 0, 5, 6. (a) Estimate lambda per hour. (b) Using that lambda, compute the probability that in a randomly chosen hour there are at least 3 occurrences.

At a school event 600 students each buy one raffle ticket; each ticket independently has a 1/500 chance of winning. Use the Poisson approximation to estimate the probability exactly two students win.

A textile manufacturer reports an average of 0.02 defects per meter of fabric. For a roll that is 100 meters long, (a) determine the appropriate lambda for modeling defects on the whole roll, and (b) compute the probability that the roll contains at least one defect.