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The Poisson Distribution is a probability distribution used to model the number of times an event occurs within a fixed time frame. Some real-life examples of the Poisson Distribution include the number of calls received by a call center in an hour, the number of cars that pass through a toll booth in an hour, the number of people waiting in line at a bank in an hour, the number of emails received in an hour, and the number of people entering a store in an hour.
The is a probability distribution that is used to model the probability that a certain number of events occur during a fixed time interval when the events are known to occur independently and with a constant mean rate.
In this article we share 5 examples of how the Poisson distribution is used in the real world.
Example 1: Calls per Hour at a Call Center
Call centers use the Poisson distribution to model the number of expected calls per hour that they’ll receive so they know how many call center reps to keep on staff.
For example, suppose a given call center receives 10 calls per hour. We can use a to find the probability that a call center receives 0, 1, 2, 3 … calls in a given hour:
- P(X = 0 calls) = 0.00005
- P(X = 1 call) = 0.00045
- P(X = 2 calls) = 0.00227
- P(X = 3 calls) = 0.00757
And so on.
This gives call center managers an idea of how many calls they’re likely to receive per hour and enables them to manage employee schedules based on the number of expected calls.
Example 2: Number of Arrivals at a Restaurant
Restaurants use the Poisson distribution to model the number of expected customers that will arrive at the restaurant per day.
For example, suppose a given restaurant receives an average of 100 customers per day. We can use the to find the probability that the restaurant receives more than a certain number of customers:
- P(X > 110 customers) = 0.14714
- P(X > 120 customers) = 0.02267
- P(X > 130 customers) = 0.00171
And so on.
This gives restaurant managers an idea of the likelihood that they’ll receive more than a certain number of customers in a given day.
Example 3: Number of Website Visitors per Hour
Website hosting companies use the Poisson distribution to model the number of expected visitors per hour that websites will receive.
For example, suppose a given website receives an average of 20 visitors per hour. We can use the to find the probability that the website receives more than a certain number of visitors in a given hour:
- P(X > 25 visitors) = 0.11218
- P(X > 30 visitors) = 0.01347
- P(X > 35 visitors) = 0.00080
And so on.
This gives hosting companies an idea of how much bandwidth to provide to different websites to ensure that they’ll be able to handle a certain number of visitors each hour.
Example 4: Number of Bankruptcies Filed per Month
Banks use the Poisson distribution to model the number of expected customer bankruptcies per month.
For example, suppose a given bank has an average of 3 bankruptcies filed by customers each month. We can use the to find the probability that the bank receives a specific number of bankruptcy files in a given month:
- P(X = 0 bankruptcies) = 0.04979
- P(X = 1 bankruptcy) = 0.14936
- P(X = 2 bankruptcies) = 0.22404
And so on.
This gives banks an idea of how much reserve cash to keep on hand in case a certain number of bankruptcies occur in a given month.
Example 5: Number of Network Failures per Week
Technology companies use the Poisson distribution to model the number of expected network failures per week.
For example, suppose a given company experiences an average of 1 network failure per week. We can use the to find the probability that the company experiences a certain number of network failures in a given week:
- P(X = 0 failures) = 0.36788
- P(X = 1 failure) = 0.36788
- P(X = 2 failures) = 0.18394
And so on.
This gives the company an idea of how many failures are likely to occur each week.